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$f (x) = 7 (x^{\frac{1}{5}} + 7)$ ; find $f^{- 1} (x)$

خطوة 1

اكتب $f (x) = 7 (x^{\frac{1}{5}} + 7)$ في صورة معادلة.

$y = 7 (x^{\frac{1}{5}} + 7)$

خطوة 2

بادِل المتغيرات.

$x = 7 (y^{\frac{1}{5}} + 7)$

خطوة 3

أوجِد قيمة $y$ .

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خطوة 3.1

أعِد كتابة المعادلة في صورة $7 (y^{\frac{1}{5}} + 7) = x$ .

$7 (y^{\frac{1}{5}} + 7) = x$

خطوة 3.2

اقسِم كل حد في $7 (y^{\frac{1}{5}} + 7) = x$ على $7$ وبسّط.

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خطوة 3.2.1

اقسِم كل حد في $7 (y^{\frac{1}{5}} + 7) = x$ على $7$ .

$\frac{7 (y^{\frac{1}{5}} + 7)}{7} = \frac{x}{7}$

خطوة 3.2.2

بسّط الطرف الأيسر.

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خطوة 3.2.2.1

ألغِ العامل المشترك.

$\frac{7 (y^{\frac{1}{5}} + 7)}{7} = \frac{x}{7}$

خطوة 3.2.2.2

اقسِم $y^{\frac{1}{5}} + 7$ على $1$ .

$y^{\frac{1}{5}} + 7 = \frac{x}{7}$

خطوة 3.3

انقُل كل الحدود التي لا تحتوي على $y$ إلى المتعادل الأيمن.

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خطوة 3.3.1

اطرح $7$ من كلا المتعادلين.

$y^{\frac{1}{5}} - \frac{x}{7} = - 7$

خطوة 3.3.2

أضف $\frac{x}{7}$ إلى كلا المتعادلين.

$y^{\frac{1}{5}} = - 7 + \frac{x}{7}$

خطوة 3.4

ارفع كل متعادل إلى القوة $5$ لحذف الأُس الكسري في الطرف الأيسر.

${(y^{\frac{1}{5}})}^{5} = {(- 7 + \frac{x}{7})}^{5}$

خطوة 3.5

بسّط الأُس.

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خطوة 3.5.1

بسّط الطرف الأيسر.

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خطوة 3.5.1.1

بسّط ${(y^{\frac{1}{5}})}^{5}$ .

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خطوة 3.5.1.1.1

اضرب الأُسس في ${(y^{\frac{1}{5}})}^{5}$ .

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خطوة 3.5.1.1.1.1

طبّق قاعدة القوة واضرب الأُسس، ${(a^{m})}^{n} = a^{m n}$ .

$y^{\frac{1}{5} \cdot 5} = {(- 7 + \frac{x}{7})}^{5}$

خطوة 3.5.1.1.1.2

ألغِ العامل المشترك لـ $5$ .

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خطوة 3.5.1.1.1.2.1

ألغِ العامل المشترك.

$y^{\frac{1}{5} \cdot 5} = {(- 7 + \frac{x}{7})}^{5}$

خطوة 3.5.1.1.1.2.2

أعِد كتابة العبارة.

$y^{1} = {(- 7 + \frac{x}{7})}^{5}$

خطوة 3.5.1.1.2

بسّط.

$y = {(- 7 + \frac{x}{7})}^{5}$

خطوة 3.5.2

بسّط الطرف الأيمن.

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خطوة 3.5.2.1

بسّط ${(- 7 + \frac{x}{7})}^{5}$ .

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خطوة 3.5.2.1.1

استخدِم مبرهنة ذات الحدين.

$y = {(- 7)}^{5} + 5 {(- 7)}^{4} \frac{x}{7} + 10 {(- 7)}^{3} {(\frac{x}{7})}^{2} + 10 {(- 7)}^{2} {(\frac{x}{7})}^{3} + 5 \cdot - 7 {(\frac{x}{7})}^{4} + {(\frac{x}{7})}^{5}$

خطوة 3.5.2.1.2

بسّط كل حد.

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خطوة 3.5.2.1.2.1

ارفع $- 7$ إلى القوة $5$ .

$y = - 16807 + 5 {(- 7)}^{4} \frac{x}{7} + 10 {(- 7)}^{3} {(\frac{x}{7})}^{2} + 10 {(- 7)}^{2} {(\frac{x}{7})}^{3} + 5 \cdot - 7 {(\frac{x}{7})}^{4} + {(\frac{x}{7})}^{5}$

خطوة 3.5.2.1.2.2

ارفع $- 7$ إلى القوة $4$ .

$y = - 16807 + 5 \cdot 2401 \frac{x}{7} + 10 {(- 7)}^{3} {(\frac{x}{7})}^{2} + 10 {(- 7)}^{2} {(\frac{x}{7})}^{3} + 5 \cdot - 7 {(\frac{x}{7})}^{4} + {(\frac{x}{7})}^{5}$

خطوة 3.5.2.1.2.3

اضرب $5$ في $2401$ .

$y = - 16807 + 12005 \frac{x}{7} + 10 {(- 7)}^{3} {(\frac{x}{7})}^{2} + 10 {(- 7)}^{2} {(\frac{x}{7})}^{3} + 5 \cdot - 7 {(\frac{x}{7})}^{4} + {(\frac{x}{7})}^{5}$

خطوة 3.5.2.1.2.4

ألغِ العامل المشترك لـ $7$ .

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خطوة 3.5.2.1.2.4.1

أخرِج العامل $7$ من $12005$ .

$y = - 16807 + 7 (1715) \frac{x}{7} + 10 {(- 7)}^{3} {(\frac{x}{7})}^{2} + 10 {(- 7)}^{2} {(\frac{x}{7})}^{3} + 5 \cdot - 7 {(\frac{x}{7})}^{4} + {(\frac{x}{7})}^{5}$

خطوة 3.5.2.1.2.4.2

ألغِ العامل المشترك.

$y = - 16807 + 7 \cdot 1715 \frac{x}{7} + 10 {(- 7)}^{3} {(\frac{x}{7})}^{2} + 10 {(- 7)}^{2} {(\frac{x}{7})}^{3} + 5 \cdot - 7 {(\frac{x}{7})}^{4} + {(\frac{x}{7})}^{5}$

خطوة 3.5.2.1.2.4.3

أعِد كتابة العبارة.

$y = - 16807 + 1715 x + 10 {(- 7)}^{3} {(\frac{x}{7})}^{2} + 10 {(- 7)}^{2} {(\frac{x}{7})}^{3} + 5 \cdot - 7 {(\frac{x}{7})}^{4} + {(\frac{x}{7})}^{5}$

خطوة 3.5.2.1.2.5

ارفع $- 7$ إلى القوة $3$ .

$y = - 16807 + 1715 x + 10 \cdot - 343 {(\frac{x}{7})}^{2} + 10 {(- 7)}^{2} {(\frac{x}{7})}^{3} + 5 \cdot - 7 {(\frac{x}{7})}^{4} + {(\frac{x}{7})}^{5}$

خطوة 3.5.2.1.2.6

اضرب $10$ في $- 343$ .

$y = - 16807 + 1715 x - 3430 {(\frac{x}{7})}^{2} + 10 {(- 7)}^{2} {(\frac{x}{7})}^{3} + 5 \cdot - 7 {(\frac{x}{7})}^{4} + {(\frac{x}{7})}^{5}$

خطوة 3.5.2.1.2.7

طبّق قاعدة الضرب على $\frac{x}{7}$ .

$y = - 16807 + 1715 x - 3430 \frac{x^{2}}{7^{2}} + 10 {(- 7)}^{2} {(\frac{x}{7})}^{3} + 5 \cdot - 7 {(\frac{x}{7})}^{4} + {(\frac{x}{7})}^{5}$

خطوة 3.5.2.1.2.8

ارفع $7$ إلى القوة $2$ .

$y = - 16807 + 1715 x - 3430 \frac{x^{2}}{49} + 10 {(- 7)}^{2} {(\frac{x}{7})}^{3} + 5 \cdot - 7 {(\frac{x}{7})}^{4} + {(\frac{x}{7})}^{5}$

خطوة 3.5.2.1.2.9

ألغِ العامل المشترك لـ $49$ .

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خطوة 3.5.2.1.2.9.1

أخرِج العامل $49$ من $- 3430$ .

$y = - 16807 + 1715 x + 49 (- 70) \frac{x^{2}}{49} + 10 {(- 7)}^{2} {(\frac{x}{7})}^{3} + 5 \cdot - 7 {(\frac{x}{7})}^{4} + {(\frac{x}{7})}^{5}$

خطوة 3.5.2.1.2.9.2

ألغِ العامل المشترك.

$y = - 16807 + 1715 x + 49 \cdot - 70 \frac{x^{2}}{49} + 10 {(- 7)}^{2} {(\frac{x}{7})}^{3} + 5 \cdot - 7 {(\frac{x}{7})}^{4} + {(\frac{x}{7})}^{5}$

خطوة 3.5.2.1.2.9.3

أعِد كتابة العبارة.

$y = - 16807 + 1715 x - 70 x^{2} + 10 {(- 7)}^{2} {(\frac{x}{7})}^{3} + 5 \cdot - 7 {(\frac{x}{7})}^{4} + {(\frac{x}{7})}^{5}$

خطوة 3.5.2.1.2.10

ارفع $- 7$ إلى القوة $2$ .

$y = - 16807 + 1715 x - 70 x^{2} + 10 \cdot 49 {(\frac{x}{7})}^{3} + 5 \cdot - 7 {(\frac{x}{7})}^{4} + {(\frac{x}{7})}^{5}$

خطوة 3.5.2.1.2.11

اضرب $10$ في $49$ .

$y = - 16807 + 1715 x - 70 x^{2} + 490 {(\frac{x}{7})}^{3} + 5 \cdot - 7 {(\frac{x}{7})}^{4} + {(\frac{x}{7})}^{5}$

خطوة 3.5.2.1.2.12

طبّق قاعدة الضرب على $\frac{x}{7}$ .

$y = - 16807 + 1715 x - 70 x^{2} + 490 \frac{x^{3}}{7^{3}} + 5 \cdot - 7 {(\frac{x}{7})}^{4} + {(\frac{x}{7})}^{5}$

خطوة 3.5.2.1.2.13

ارفع $7$ إلى القوة $3$ .

$y = - 16807 + 1715 x - 70 x^{2} + 490 \frac{x^{3}}{343} + 5 \cdot - 7 {(\frac{x}{7})}^{4} + {(\frac{x}{7})}^{5}$

خطوة 3.5.2.1.2.14

ألغِ العامل المشترك لـ $49$ .

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خطوة 3.5.2.1.2.14.1

أخرِج العامل $49$ من $490$ .

$y = - 16807 + 1715 x - 70 x^{2} + 49 (10) \frac{x^{3}}{343} + 5 \cdot - 7 {(\frac{x}{7})}^{4} + {(\frac{x}{7})}^{5}$

خطوة 3.5.2.1.2.14.2

أخرِج العامل $49$ من $343$ .

$y = - 16807 + 1715 x - 70 x^{2} + 49 \cdot 10 \frac{x^{3}}{49 \cdot 7} + 5 \cdot - 7 {(\frac{x}{7})}^{4} + {(\frac{x}{7})}^{5}$

خطوة 3.5.2.1.2.14.3

ألغِ العامل المشترك.

$y = - 16807 + 1715 x - 70 x^{2} + 49 \cdot 10 \frac{x^{3}}{49 \cdot 7} + 5 \cdot - 7 {(\frac{x}{7})}^{4} + {(\frac{x}{7})}^{5}$

خطوة 3.5.2.1.2.14.4

أعِد كتابة العبارة.

$y = - 16807 + 1715 x - 70 x^{2} + 10 \frac{x^{3}}{7} + 5 \cdot - 7 {(\frac{x}{7})}^{4} + {(\frac{x}{7})}^{5}$

خطوة 3.5.2.1.2.15

اجمع $10$ و $\frac{x^{3}}{7}$ .

$y = - 16807 + 1715 x - 70 x^{2} + \frac{10 x^{3}}{7} + 5 \cdot - 7 {(\frac{x}{7})}^{4} + {(\frac{x}{7})}^{5}$

خطوة 3.5.2.1.2.16

اضرب $5$ في $- 7$ .

$y = - 16807 + 1715 x - 70 x^{2} + \frac{10 x^{3}}{7} - 35 {(\frac{x}{7})}^{4} + {(\frac{x}{7})}^{5}$

خطوة 3.5.2.1.2.17

طبّق قاعدة الضرب على $\frac{x}{7}$ .

$y = - 16807 + 1715 x - 70 x^{2} + \frac{10 x^{3}}{7} - 35 \frac{x^{4}}{7^{4}} + {(\frac{x}{7})}^{5}$

خطوة 3.5.2.1.2.18

ارفع $7$ إلى القوة $4$ .

$y = - 16807 + 1715 x - 70 x^{2} + \frac{10 x^{3}}{7} - 35 \frac{x^{4}}{2401} + {(\frac{x}{7})}^{5}$

خطوة 3.5.2.1.2.19

ألغِ العامل المشترك لـ $7$ .

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خطوة 3.5.2.1.2.19.1

أخرِج العامل $7$ من $- 35$ .

$y = - 16807 + 1715 x - 70 x^{2} + \frac{10 x^{3}}{7} + 7 (- 5) \frac{x^{4}}{2401} + {(\frac{x}{7})}^{5}$

خطوة 3.5.2.1.2.19.2

أخرِج العامل $7$ من $2401$ .

$y = - 16807 + 1715 x - 70 x^{2} + \frac{10 x^{3}}{7} + 7 \cdot - 5 \frac{x^{4}}{7 \cdot 343} + {(\frac{x}{7})}^{5}$

خطوة 3.5.2.1.2.19.3

ألغِ العامل المشترك.

$y = - 16807 + 1715 x - 70 x^{2} + \frac{10 x^{3}}{7} + 7 \cdot - 5 \frac{x^{4}}{7 \cdot 343} + {(\frac{x}{7})}^{5}$

خطوة 3.5.2.1.2.19.4

أعِد كتابة العبارة.

$y = - 16807 + 1715 x - 70 x^{2} + \frac{10 x^{3}}{7} - 5 \frac{x^{4}}{343} + {(\frac{x}{7})}^{5}$

خطوة 3.5.2.1.2.20

اجمع $- 5$ و $\frac{x^{4}}{343}$ .

$y = - 16807 + 1715 x - 70 x^{2} + \frac{10 x^{3}}{7} + \frac{- 5 x^{4}}{343} + {(\frac{x}{7})}^{5}$

خطوة 3.5.2.1.2.21

انقُل السالب أمام الكسر.

$y = - 16807 + 1715 x - 70 x^{2} + \frac{10 x^{3}}{7} - \frac{5 x^{4}}{343} + {(\frac{x}{7})}^{5}$

خطوة 3.5.2.1.2.22

طبّق قاعدة الضرب على $\frac{x}{7}$ .

$y = - 16807 + 1715 x - 70 x^{2} + \frac{10 x^{3}}{7} - \frac{5 x^{4}}{343} + \frac{x^{5}}{7^{5}}$

خطوة 3.5.2.1.2.23

ارفع $7$ إلى القوة $5$ .

$y = - 16807 + 1715 x - 70 x^{2} + \frac{10 x^{3}}{7} - \frac{5 x^{4}}{343} + \frac{x^{5}}{16807}$

خطوة 3.6

بسّط $- 16807 + 1715 x - 70 x^{2} + \frac{10 x^{3}}{7} - \frac{5 x^{4}}{343} + \frac{x^{5}}{16807}$ .

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خطوة 3.6.1

انقُل $- 16807$ .

$y = 1715 x - 70 x^{2} + \frac{10 x^{3}}{7} - \frac{5 x^{4}}{343} + \frac{x^{5}}{16807} - 16807$

خطوة 3.6.2

انقُل $1715 x$ .

$y = - 70 x^{2} + \frac{10 x^{3}}{7} - \frac{5 x^{4}}{343} + \frac{x^{5}}{16807} + 1715 x - 16807$

خطوة 3.6.3

انقُل $- 70 x^{2}$ .

$y = \frac{10 x^{3}}{7} - \frac{5 x^{4}}{343} + \frac{x^{5}}{16807} - 70 x^{2} + 1715 x - 16807$

خطوة 3.6.4

انقُل $\frac{10 x^{3}}{7}$ .

$y = - \frac{5 x^{4}}{343} + \frac{x^{5}}{16807} + \frac{10 x^{3}}{7} - 70 x^{2} + 1715 x - 16807$

خطوة 3.6.5

أعِد ترتيب $- \frac{5 x^{4}}{343}$ و $\frac{x^{5}}{16807}$ .

$y = \frac{x^{5}}{16807} - \frac{5 x^{4}}{343} + \frac{10 x^{3}}{7} - 70 x^{2} + 1715 x - 16807$

خطوة 4

استبدِل $y$ بـ $f^{- 1} (x)$ لعرض الإجابة النهائية.

$f^{- 1} (x) = \frac{x^{5}}{16807} - \frac{5 x^{4}}{343} + \frac{10 x^{3}}{7} - 70 x^{2} + 1715 x - 16807$

خطوة 5

تحقق مما إذا كانت $f^{- 1} (x) = \frac{x^{5}}{16807} - \frac{5 x^{4}}{343} + \frac{10 x^{3}}{7} - 70 x^{2} + 1715 x - 16807$ هي معكوس $f (x) = 7 (x^{\frac{1}{5}} + 7)$ .

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خطوة 5.1

للتحقق من صحة المعكوس، تحقق مما إذا كانتا $f^{- 1} (f (x)) = x$ و $f (f^{- 1} (x)) = x$ .

خطوة 5.2

احسِب قيمة $f^{- 1} (f (x))$ .

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خطوة 5.2.1

عيّن دالة النتيجة المركّبة.

$f^{- 1} (f (x))$

خطوة 5.2.2

احسِب قيمة $f^{- 1} (7 (x^{\frac{1}{5}} + 7))$ باستبدال قيمة $f$ في $f^{- 1}$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = \frac{{(7 (x^{\frac{1}{5}} + 7))}^{5}}{16807} - \frac{5 {(7 (x^{\frac{1}{5}} + 7))}^{4}}{343} + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3

بسّط كل حد.

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خطوة 5.2.3.1

بسّط بَسْط الكسر.

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خطوة 5.2.3.1.1

طبّق قاعدة الضرب على $7 (x^{\frac{1}{5}} + 7)$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = \frac{7^{5} {(x^{\frac{1}{5}} + 7)}^{5}}{16807} - \frac{5 {(7 (x^{\frac{1}{5}} + 7))}^{4}}{343} + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.1.2

ارفع $7$ إلى القوة $5$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = \frac{16807 {(x^{\frac{1}{5}} + 7)}^{5}}{16807} - \frac{5 {(7 (x^{\frac{1}{5}} + 7))}^{4}}{343} + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.2

ألغِ العامل المشترك.

خطوة 5.2.3.3

اقسِم ${(x^{\frac{1}{5}} + 7)}^{5}$ على $1$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = {(x^{\frac{1}{5}} + 7)}^{5} - \frac{5 {(7 (x^{\frac{1}{5}} + 7))}^{4}}{343} + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.4

استخدِم مبرهنة ذات الحدين.

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = {(x^{\frac{1}{5}})}^{5} + 5 {(x^{\frac{1}{5}})}^{4} \cdot 7 + 10 {(x^{\frac{1}{5}})}^{3} \cdot 7^{2} + 10 {(x^{\frac{1}{5}})}^{2} \cdot 7^{3} + 5 x^{\frac{1}{5}} \cdot 7^{4} + 7^{5} - \frac{5 {(7 (x^{\frac{1}{5}} + 7))}^{4}}{343} + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.5

بسّط كل حد.

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خطوة 5.2.3.5.1

اضرب الأُسس في ${(x^{\frac{1}{5}})}^{5}$ .

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خطوة 5.2.3.5.1.1

طبّق قاعدة القوة واضرب الأُسس، ${(a^{m})}^{n} = a^{m n}$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x^{\frac{1}{5} \cdot 5} + 5 {(x^{\frac{1}{5}})}^{4} \cdot 7 + 10 {(x^{\frac{1}{5}})}^{3} \cdot 7^{2} + 10 {(x^{\frac{1}{5}})}^{2} \cdot 7^{3} + 5 x^{\frac{1}{5}} \cdot 7^{4} + 7^{5} - \frac{5 {(7 (x^{\frac{1}{5}} + 7))}^{4}}{343} + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.5.1.2

ألغِ العامل المشترك لـ $5$ .

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خطوة 5.2.3.5.1.2.1

ألغِ العامل المشترك.

خطوة 5.2.3.5.1.2.2

أعِد كتابة العبارة.

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 5 {(x^{\frac{1}{5}})}^{4} \cdot 7 + 10 {(x^{\frac{1}{5}})}^{3} \cdot 7^{2} + 10 {(x^{\frac{1}{5}})}^{2} \cdot 7^{3} + 5 x^{\frac{1}{5}} \cdot 7^{4} + 7^{5} - \frac{5 {(7 (x^{\frac{1}{5}} + 7))}^{4}}{343} + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.5.2

بسّط.

خطوة 5.2.3.5.3

اضرب الأُسس في ${(x^{\frac{1}{5}})}^{4}$ .

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خطوة 5.2.3.5.3.1

طبّق قاعدة القوة واضرب الأُسس، ${(a^{m})}^{n} = a^{m n}$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 5 x^{\frac{1}{5} \cdot 4} \cdot 7 + 10 {(x^{\frac{1}{5}})}^{3} \cdot 7^{2} + 10 {(x^{\frac{1}{5}})}^{2} \cdot 7^{3} + 5 x^{\frac{1}{5}} \cdot 7^{4} + 7^{5} - \frac{5 {(7 (x^{\frac{1}{5}} + 7))}^{4}}{343} + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.5.3.2

اجمع $\frac{1}{5}$ و $4$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 5 x^{\frac{4}{5}} \cdot 7 + 10 {(x^{\frac{1}{5}})}^{3} \cdot 7^{2} + 10 {(x^{\frac{1}{5}})}^{2} \cdot 7^{3} + 5 x^{\frac{1}{5}} \cdot 7^{4} + 7^{5} - \frac{5 {(7 (x^{\frac{1}{5}} + 7))}^{4}}{343} + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.5.4

اضرب $7$ في $5$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 10 {(x^{\frac{1}{5}})}^{3} \cdot 7^{2} + 10 {(x^{\frac{1}{5}})}^{2} \cdot 7^{3} + 5 x^{\frac{1}{5}} \cdot 7^{4} + 7^{5} - \frac{5 {(7 (x^{\frac{1}{5}} + 7))}^{4}}{343} + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.5.5

اضرب الأُسس في ${(x^{\frac{1}{5}})}^{3}$ .

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خطوة 5.2.3.5.5.1

طبّق قاعدة القوة واضرب الأُسس، ${(a^{m})}^{n} = a^{m n}$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 10 x^{\frac{1}{5} \cdot 3} \cdot 7^{2} + 10 {(x^{\frac{1}{5}})}^{2} \cdot 7^{3} + 5 x^{\frac{1}{5}} \cdot 7^{4} + 7^{5} - \frac{5 {(7 (x^{\frac{1}{5}} + 7))}^{4}}{343} + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.5.5.2

اجمع $\frac{1}{5}$ و $3$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 10 x^{\frac{3}{5}} \cdot 7^{2} + 10 {(x^{\frac{1}{5}})}^{2} \cdot 7^{3} + 5 x^{\frac{1}{5}} \cdot 7^{4} + 7^{5} - \frac{5 {(7 (x^{\frac{1}{5}} + 7))}^{4}}{343} + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.5.6

ارفع $7$ إلى القوة $2$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 10 x^{\frac{3}{5}} \cdot 49 + 10 {(x^{\frac{1}{5}})}^{2} \cdot 7^{3} + 5 x^{\frac{1}{5}} \cdot 7^{4} + 7^{5} - \frac{5 {(7 (x^{\frac{1}{5}} + 7))}^{4}}{343} + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.5.7

اضرب $49$ في $10$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 10 {(x^{\frac{1}{5}})}^{2} \cdot 7^{3} + 5 x^{\frac{1}{5}} \cdot 7^{4} + 7^{5} - \frac{5 {(7 (x^{\frac{1}{5}} + 7))}^{4}}{343} + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.5.8

اضرب الأُسس في ${(x^{\frac{1}{5}})}^{2}$ .

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خطوة 5.2.3.5.8.1

طبّق قاعدة القوة واضرب الأُسس، ${(a^{m})}^{n} = a^{m n}$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 10 x^{\frac{1}{5} \cdot 2} \cdot 7^{3} + 5 x^{\frac{1}{5}} \cdot 7^{4} + 7^{5} - \frac{5 {(7 (x^{\frac{1}{5}} + 7))}^{4}}{343} + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.5.8.2

اجمع $\frac{1}{5}$ و $2$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 10 x^{\frac{2}{5}} \cdot 7^{3} + 5 x^{\frac{1}{5}} \cdot 7^{4} + 7^{5} - \frac{5 {(7 (x^{\frac{1}{5}} + 7))}^{4}}{343} + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.5.9

ارفع $7$ إلى القوة $3$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 10 x^{\frac{2}{5}} \cdot 343 + 5 x^{\frac{1}{5}} \cdot 7^{4} + 7^{5} - \frac{5 {(7 (x^{\frac{1}{5}} + 7))}^{4}}{343} + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.5.10

اضرب $343$ في $10$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 5 x^{\frac{1}{5}} \cdot 7^{4} + 7^{5} - \frac{5 {(7 (x^{\frac{1}{5}} + 7))}^{4}}{343} + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.5.11

ارفع $7$ إلى القوة $4$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 5 x^{\frac{1}{5}} \cdot 2401 + 7^{5} - \frac{5 {(7 (x^{\frac{1}{5}} + 7))}^{4}}{343} + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.5.12

اضرب $2401$ في $5$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 7^{5} - \frac{5 {(7 (x^{\frac{1}{5}} + 7))}^{4}}{343} + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.5.13

ارفع $7$ إلى القوة $5$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - \frac{5 {(7 (x^{\frac{1}{5}} + 7))}^{4}}{343} + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.6

بسّط بَسْط الكسر.

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خطوة 5.2.3.6.1

طبّق قاعدة الضرب على $7 (x^{\frac{1}{5}} + 7)$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - \frac{5 \cdot (7^{4} {(x^{\frac{1}{5}} + 7)}^{4})}{343} + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.6.2

ارفع $7$ إلى القوة $4$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - \frac{5 \cdot (2401 {(x^{\frac{1}{5}} + 7)}^{4})}{343} + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.6.3

اضرب $5$ في $2401$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - \frac{12005 {(x^{\frac{1}{5}} + 7)}^{4}}{343} + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.7

أخرِج العامل $343$ من $12005 {(x^{\frac{1}{5}} + 7)}^{4}$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - \frac{343 (35 {(x^{\frac{1}{5}} + 7)}^{4})}{343} + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.8

ألغِ العوامل المشتركة.

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خطوة 5.2.3.8.1

أخرِج العامل $343$ من $343$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - \frac{343 (35 {(x^{\frac{1}{5}} + 7)}^{4})}{343 (1)} + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.8.2

ألغِ العامل المشترك.

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - \frac{343 (35 {(x^{\frac{1}{5}} + 7)}^{4})}{343 \cdot 1} + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.8.3

أعِد كتابة العبارة.

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - \frac{35 {(x^{\frac{1}{5}} + 7)}^{4}}{1} + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.8.4

اقسِم $35 {(x^{\frac{1}{5}} + 7)}^{4}$ على $1$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - (35 {(x^{\frac{1}{5}} + 7)}^{4}) + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.9

استخدِم مبرهنة ذات الحدين.

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - (35 ({(x^{\frac{1}{5}})}^{4} + 4 {(x^{\frac{1}{5}})}^{3} \cdot 7 + 6 {(x^{\frac{1}{5}})}^{2} \cdot 7^{2} + 4 x^{\frac{1}{5}} \cdot 7^{3} + 7^{4})) + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.10

بسّط كل حد.

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خطوة 5.2.3.10.1

اضرب الأُسس في ${(x^{\frac{1}{5}})}^{4}$ .

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خطوة 5.2.3.10.1.1

طبّق قاعدة القوة واضرب الأُسس، ${(a^{m})}^{n} = a^{m n}$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - (35 (x^{\frac{1}{5} \cdot 4} + 4 {(x^{\frac{1}{5}})}^{3} \cdot 7 + 6 {(x^{\frac{1}{5}})}^{2} \cdot 7^{2} + 4 x^{\frac{1}{5}} \cdot 7^{3} + 7^{4})) + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.10.1.2

اجمع $\frac{1}{5}$ و $4$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - (35 (x^{\frac{4}{5}} + 4 {(x^{\frac{1}{5}})}^{3} \cdot 7 + 6 {(x^{\frac{1}{5}})}^{2} \cdot 7^{2} + 4 x^{\frac{1}{5}} \cdot 7^{3} + 7^{4})) + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.10.2

اضرب الأُسس في ${(x^{\frac{1}{5}})}^{3}$ .

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خطوة 5.2.3.10.2.1

طبّق قاعدة القوة واضرب الأُسس، ${(a^{m})}^{n} = a^{m n}$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - (35 (x^{\frac{4}{5}} + 4 x^{\frac{1}{5} \cdot 3} \cdot 7 + 6 {(x^{\frac{1}{5}})}^{2} \cdot 7^{2} + 4 x^{\frac{1}{5}} \cdot 7^{3} + 7^{4})) + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.10.2.2

اجمع $\frac{1}{5}$ و $3$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - (35 (x^{\frac{4}{5}} + 4 x^{\frac{3}{5}} \cdot 7 + 6 {(x^{\frac{1}{5}})}^{2} \cdot 7^{2} + 4 x^{\frac{1}{5}} \cdot 7^{3} + 7^{4})) + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.10.3

اضرب $7$ في $4$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - (35 (x^{\frac{4}{5}} + 28 x^{\frac{3}{5}} + 6 {(x^{\frac{1}{5}})}^{2} \cdot 7^{2} + 4 x^{\frac{1}{5}} \cdot 7^{3} + 7^{4})) + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.10.4

اضرب الأُسس في ${(x^{\frac{1}{5}})}^{2}$ .

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خطوة 5.2.3.10.4.1

طبّق قاعدة القوة واضرب الأُسس، ${(a^{m})}^{n} = a^{m n}$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - (35 (x^{\frac{4}{5}} + 28 x^{\frac{3}{5}} + 6 x^{\frac{1}{5} \cdot 2} \cdot 7^{2} + 4 x^{\frac{1}{5}} \cdot 7^{3} + 7^{4})) + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.10.4.2

اجمع $\frac{1}{5}$ و $2$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - (35 (x^{\frac{4}{5}} + 28 x^{\frac{3}{5}} + 6 x^{\frac{2}{5}} \cdot 7^{2} + 4 x^{\frac{1}{5}} \cdot 7^{3} + 7^{4})) + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.10.5

ارفع $7$ إلى القوة $2$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - (35 (x^{\frac{4}{5}} + 28 x^{\frac{3}{5}} + 6 x^{\frac{2}{5}} \cdot 49 + 4 x^{\frac{1}{5}} \cdot 7^{3} + 7^{4})) + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.10.6

اضرب $49$ في $6$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - (35 (x^{\frac{4}{5}} + 28 x^{\frac{3}{5}} + 294 x^{\frac{2}{5}} + 4 x^{\frac{1}{5}} \cdot 7^{3} + 7^{4})) + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.10.7

ارفع $7$ إلى القوة $3$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - (35 (x^{\frac{4}{5}} + 28 x^{\frac{3}{5}} + 294 x^{\frac{2}{5}} + 4 x^{\frac{1}{5}} \cdot 343 + 7^{4})) + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.10.8

اضرب $343$ في $4$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - (35 (x^{\frac{4}{5}} + 28 x^{\frac{3}{5}} + 294 x^{\frac{2}{5}} + 1372 x^{\frac{1}{5}} + 7^{4})) + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.10.9

ارفع $7$ إلى القوة $4$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - (35 (x^{\frac{4}{5}} + 28 x^{\frac{3}{5}} + 294 x^{\frac{2}{5}} + 1372 x^{\frac{1}{5}} + 2401)) + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.11

طبّق خاصية التوزيع.

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - (35 x^{\frac{4}{5}} + 35 (28 x^{\frac{3}{5}}) + 35 (294 x^{\frac{2}{5}}) + 35 (1372 x^{\frac{1}{5}}) + 35 \cdot 2401) + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.12

بسّط.

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خطوة 5.2.3.12.1

اضرب $28$ في $35$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - (35 x^{\frac{4}{5}} + 980 x^{\frac{3}{5}} + 35 (294 x^{\frac{2}{5}}) + 35 (1372 x^{\frac{1}{5}}) + 35 \cdot 2401) + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.12.2

اضرب $294$ في $35$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - (35 x^{\frac{4}{5}} + 980 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 35 (1372 x^{\frac{1}{5}}) + 35 \cdot 2401) + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.12.3

اضرب $1372$ في $35$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - (35 x^{\frac{4}{5}} + 980 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 48020 x^{\frac{1}{5}} + 35 \cdot 2401) + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.12.4

اضرب $35$ في $2401$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - (35 x^{\frac{4}{5}} + 980 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 48020 x^{\frac{1}{5}} + 84035) + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.13

طبّق خاصية التوزيع.

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - (35 x^{\frac{4}{5}}) - (980 x^{\frac{3}{5}}) - (10290 x^{\frac{2}{5}}) - (48020 x^{\frac{1}{5}}) - 1 \cdot 84035 + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.14

بسّط.

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خطوة 5.2.3.14.1

اضرب $35$ في $- 1$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - (980 x^{\frac{3}{5}}) - (10290 x^{\frac{2}{5}}) - (48020 x^{\frac{1}{5}}) - 1 \cdot 84035 + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.14.2

اضرب $980$ في $- 1$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - (10290 x^{\frac{2}{5}}) - (48020 x^{\frac{1}{5}}) - 1 \cdot 84035 + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.14.3

اضرب $10290$ في $- 1$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - (48020 x^{\frac{1}{5}}) - 1 \cdot 84035 + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.14.4

اضرب $48020$ في $- 1$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 1 \cdot 84035 + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.14.5

اضرب $- 1$ في $84035$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + \frac{10 {(7 (x^{\frac{1}{5}} + 7))}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.15

بسّط بَسْط الكسر.

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خطوة 5.2.3.15.1

طبّق قاعدة الضرب على $7 (x^{\frac{1}{5}} + 7)$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + \frac{10 \cdot (7^{3} {(x^{\frac{1}{5}} + 7)}^{3})}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.15.2

ارفع $7$ إلى القوة $3$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + \frac{10 \cdot (343 {(x^{\frac{1}{5}} + 7)}^{3})}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.15.3

اضرب $10$ في $343$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + \frac{3430 {(x^{\frac{1}{5}} + 7)}^{3}}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.16

أخرِج العامل $7$ من $3430 {(x^{\frac{1}{5}} + 7)}^{3}$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + \frac{7 (490 {(x^{\frac{1}{5}} + 7)}^{3})}{7} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.17

ألغِ العوامل المشتركة.

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خطوة 5.2.3.17.1

أخرِج العامل $7$ من $7$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + \frac{7 (490 {(x^{\frac{1}{5}} + 7)}^{3})}{7 (1)} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.17.2

ألغِ العامل المشترك.

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + \frac{7 (490 {(x^{\frac{1}{5}} + 7)}^{3})}{7 \cdot 1} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.17.3

أعِد كتابة العبارة.

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + \frac{490 {(x^{\frac{1}{5}} + 7)}^{3}}{1} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.17.4

اقسِم $490 {(x^{\frac{1}{5}} + 7)}^{3}$ على $1$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 {(x^{\frac{1}{5}} + 7)}^{3} - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.18

استخدِم مبرهنة ذات الحدين.

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 ({(x^{\frac{1}{5}})}^{3} + 3 {(x^{\frac{1}{5}})}^{2} \cdot 7 + 3 x^{\frac{1}{5}} \cdot 7^{2} + 7^{3}) - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.19

بسّط كل حد.

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خطوة 5.2.3.19.1

اضرب الأُسس في ${(x^{\frac{1}{5}})}^{3}$ .

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خطوة 5.2.3.19.1.1

طبّق قاعدة القوة واضرب الأُسس، ${(a^{m})}^{n} = a^{m n}$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 (x^{\frac{1}{5} \cdot 3} + 3 {(x^{\frac{1}{5}})}^{2} \cdot 7 + 3 x^{\frac{1}{5}} \cdot 7^{2} + 7^{3}) - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.19.1.2

اجمع $\frac{1}{5}$ و $3$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 (x^{\frac{3}{5}} + 3 {(x^{\frac{1}{5}})}^{2} \cdot 7 + 3 x^{\frac{1}{5}} \cdot 7^{2} + 7^{3}) - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.19.2

اضرب الأُسس في ${(x^{\frac{1}{5}})}^{2}$ .

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خطوة 5.2.3.19.2.1

طبّق قاعدة القوة واضرب الأُسس، ${(a^{m})}^{n} = a^{m n}$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 (x^{\frac{3}{5}} + 3 x^{\frac{1}{5} \cdot 2} \cdot 7 + 3 x^{\frac{1}{5}} \cdot 7^{2} + 7^{3}) - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.19.2.2

اجمع $\frac{1}{5}$ و $2$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 (x^{\frac{3}{5}} + 3 x^{\frac{2}{5}} \cdot 7 + 3 x^{\frac{1}{5}} \cdot 7^{2} + 7^{3}) - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.19.3

اضرب $7$ في $3$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 (x^{\frac{3}{5}} + 21 x^{\frac{2}{5}} + 3 x^{\frac{1}{5}} \cdot 7^{2} + 7^{3}) - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.19.4

ارفع $7$ إلى القوة $2$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 (x^{\frac{3}{5}} + 21 x^{\frac{2}{5}} + 3 x^{\frac{1}{5}} \cdot 49 + 7^{3}) - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.19.5

اضرب $49$ في $3$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 (x^{\frac{3}{5}} + 21 x^{\frac{2}{5}} + 147 x^{\frac{1}{5}} + 7^{3}) - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.19.6

ارفع $7$ إلى القوة $3$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 (x^{\frac{3}{5}} + 21 x^{\frac{2}{5}} + 147 x^{\frac{1}{5}} + 343) - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.20

طبّق خاصية التوزيع.

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 490 (21 x^{\frac{2}{5}}) + 490 (147 x^{\frac{1}{5}}) + 490 \cdot 343 - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.21

بسّط.

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خطوة 5.2.3.21.1

اضرب $21$ في $490$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 490 (147 x^{\frac{1}{5}}) + 490 \cdot 343 - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.21.2

اضرب $147$ في $490$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 72030 x^{\frac{1}{5}} + 490 \cdot 343 - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.21.3

اضرب $490$ في $343$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 70 {(7 (x^{\frac{1}{5}} + 7))}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.22

طبّق خاصية التوزيع.

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 70 {(7 x^{\frac{1}{5}} + 7 \cdot 7)}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.23

اضرب $7$ في $7$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 70 {(7 x^{\frac{1}{5}} + 49)}^{2} + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.24

أعِد كتابة ${(7 x^{\frac{1}{5}} + 49)}^{2}$ بالصيغة $(7 x^{\frac{1}{5}} + 49) (7 x^{\frac{1}{5}} + 49)$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 70 ((7 x^{\frac{1}{5}} + 49) (7 x^{\frac{1}{5}} + 49)) + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.25

وسّع $(7 x^{\frac{1}{5}} + 49) (7 x^{\frac{1}{5}} + 49)$ باستخدام طريقة "الأول، الخارجي، الداخلي، الأخير".

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خطوة 5.2.3.25.1

طبّق خاصية التوزيع.

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 70 (7 x^{\frac{1}{5}} (7 x^{\frac{1}{5}} + 49) + 49 (7 x^{\frac{1}{5}} + 49)) + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.25.2

طبّق خاصية التوزيع.

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 70 (7 x^{\frac{1}{5}} (7 x^{\frac{1}{5}}) + 7 x^{\frac{1}{5}} \cdot 49 + 49 (7 x^{\frac{1}{5}} + 49)) + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.25.3

طبّق خاصية التوزيع.

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 70 (7 x^{\frac{1}{5}} (7 x^{\frac{1}{5}}) + 7 x^{\frac{1}{5}} \cdot 49 + 49 (7 x^{\frac{1}{5}}) + 49 \cdot 49) + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.26

بسّط ووحّد الحدود المتشابهة.

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خطوة 5.2.3.26.1

بسّط كل حد.

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خطوة 5.2.3.26.1.1

أعِد الكتابة باستخدام خاصية الإبدال لعملية الضرب.

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 70 (7 \cdot (7 x^{\frac{1}{5}} x^{\frac{1}{5}}) + 7 x^{\frac{1}{5}} \cdot 49 + 49 (7 x^{\frac{1}{5}}) + 49 \cdot 49) + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.26.1.2

اضرب $x^{\frac{1}{5}}$ في $x^{\frac{1}{5}}$ بجمع الأُسس.

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خطوة 5.2.3.26.1.2.1

انقُل $x^{\frac{1}{5}}$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 70 (7 \cdot (7 (x^{\frac{1}{5}} x^{\frac{1}{5}})) + 7 x^{\frac{1}{5}} \cdot 49 + 49 (7 x^{\frac{1}{5}}) + 49 \cdot 49) + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.26.1.2.2

استخدِم قاعدة القوة $a^{m} a^{n} = a^{m + n}$ لتجميع الأُسس.

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 70 (7 \cdot (7 x^{\frac{1}{5} + \frac{1}{5}}) + 7 x^{\frac{1}{5}} \cdot 49 + 49 (7 x^{\frac{1}{5}}) + 49 \cdot 49) + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.26.1.2.3

اجمع البسوط على القاسم المشترك.

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 70 (7 \cdot (7 x^{\frac{1 + 1}{5}}) + 7 x^{\frac{1}{5}} \cdot 49 + 49 (7 x^{\frac{1}{5}}) + 49 \cdot 49) + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.26.1.2.4

أضف $1$ و $1$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 70 (7 \cdot (7 x^{\frac{2}{5}}) + 7 x^{\frac{1}{5}} \cdot 49 + 49 (7 x^{\frac{1}{5}}) + 49 \cdot 49) + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.26.1.3

اضرب $7$ في $7$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 70 (49 x^{\frac{2}{5}} + 7 x^{\frac{1}{5}} \cdot 49 + 49 (7 x^{\frac{1}{5}}) + 49 \cdot 49) + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.26.1.4

اضرب $49$ في $7$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 70 (49 x^{\frac{2}{5}} + 343 x^{\frac{1}{5}} + 49 (7 x^{\frac{1}{5}}) + 49 \cdot 49) + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.26.1.5

اضرب $7$ في $49$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 70 (49 x^{\frac{2}{5}} + 343 x^{\frac{1}{5}} + 343 x^{\frac{1}{5}} + 49 \cdot 49) + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.26.1.6

اضرب $49$ في $49$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 70 (49 x^{\frac{2}{5}} + 343 x^{\frac{1}{5}} + 343 x^{\frac{1}{5}} + 2401) + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.26.2

أضف $343 x^{\frac{1}{5}}$ و $343 x^{\frac{1}{5}}$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 70 (49 x^{\frac{2}{5}} + 686 x^{\frac{1}{5}} + 2401) + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.27

طبّق خاصية التوزيع.

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 70 (49 x^{\frac{2}{5}}) - 70 (686 x^{\frac{1}{5}}) - 70 \cdot 2401 + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.28

بسّط.

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خطوة 5.2.3.28.1

اضرب $49$ في $- 70$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 3430 x^{\frac{2}{5}} - 70 (686 x^{\frac{1}{5}}) - 70 \cdot 2401 + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.28.2

اضرب $686$ في $- 70$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 3430 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 70 \cdot 2401 + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.28.3

اضرب $- 70$ في $2401$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 3430 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 168070 + 1715 (7 (x^{\frac{1}{5}} + 7)) - 16807$

خطوة 5.2.3.29

طبّق خاصية التوزيع.

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 3430 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 168070 + 1715 (7 x^{\frac{1}{5}} + 7 \cdot 7) - 16807$

خطوة 5.2.3.30

اضرب $7$ في $7$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 3430 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 168070 + 1715 (7 x^{\frac{1}{5}} + 49) - 16807$

خطوة 5.2.3.31

طبّق خاصية التوزيع.

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 3430 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 168070 + 1715 (7 x^{\frac{1}{5}}) + 1715 \cdot 49 - 16807$

خطوة 5.2.3.32

اضرب $7$ في $1715$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 3430 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 168070 + 12005 x^{\frac{1}{5}} + 1715 \cdot 49 - 16807$

خطوة 5.2.3.33

اضرب $1715$ في $49$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 3430 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 168070 + 12005 x^{\frac{1}{5}} + 84035 - 16807$

خطوة 5.2.4

بسّط بجمع الحدود.

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خطوة 5.2.4.1

جمّع الحدود المتعاكسة في $x + 35 x^{\frac{4}{5}} + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 35 x^{\frac{4}{5}} - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 3430 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 168070 + 12005 x^{\frac{1}{5}} + 84035 - 16807$ .

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خطوة 5.2.4.1.1

اطرح $35 x^{\frac{4}{5}}$ من $35 x^{\frac{4}{5}}$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 + 0 - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 3430 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 168070 + 12005 x^{\frac{1}{5}} + 84035 - 16807$

خطوة 5.2.4.1.2

أضف $x + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807$ و $0$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 980 x^{\frac{3}{5}} - 10290 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 10290 x^{\frac{2}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 3430 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 168070 + 12005 x^{\frac{1}{5}} + 84035 - 16807$

خطوة 5.2.4.1.3

أضف $- 10290 x^{\frac{2}{5}}$ و $10290 x^{\frac{2}{5}}$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 980 x^{\frac{3}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 0 + 72030 x^{\frac{1}{5}} + 168070 - 3430 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 168070 + 12005 x^{\frac{1}{5}} + 84035 - 16807$

خطوة 5.2.4.1.4

أضف $x + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 980 x^{\frac{3}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}}$ و $0$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 490 x^{\frac{3}{5}} + 3430 x^{\frac{2}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 980 x^{\frac{3}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 3430 x^{\frac{2}{5}} - 48020 x^{\frac{1}{5}} - 168070 + 12005 x^{\frac{1}{5}} + 84035 - 16807$

خطوة 5.2.4.1.5

اطرح $3430 x^{\frac{2}{5}}$ من $3430 x^{\frac{2}{5}}$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 490 x^{\frac{3}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 980 x^{\frac{3}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 72030 x^{\frac{1}{5}} + 168070 + 0 - 48020 x^{\frac{1}{5}} - 168070 + 12005 x^{\frac{1}{5}} + 84035 - 16807$

خطوة 5.2.4.1.6

أضف $x + 490 x^{\frac{3}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 980 x^{\frac{3}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 72030 x^{\frac{1}{5}} + 168070$ و $0$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 490 x^{\frac{3}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 980 x^{\frac{3}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 72030 x^{\frac{1}{5}} + 168070 - 48020 x^{\frac{1}{5}} - 168070 + 12005 x^{\frac{1}{5}} + 84035 - 16807$

خطوة 5.2.4.1.7

اطرح $168070$ من $168070$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 490 x^{\frac{3}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 980 x^{\frac{3}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 72030 x^{\frac{1}{5}} - 48020 x^{\frac{1}{5}} + 0 + 12005 x^{\frac{1}{5}} + 84035 - 16807$

خطوة 5.2.4.1.8

أضف $x + 490 x^{\frac{3}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 980 x^{\frac{3}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 72030 x^{\frac{1}{5}} - 48020 x^{\frac{1}{5}}$ و $0$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 490 x^{\frac{3}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 980 x^{\frac{3}{5}} - 48020 x^{\frac{1}{5}} - 84035 + 490 x^{\frac{3}{5}} + 72030 x^{\frac{1}{5}} - 48020 x^{\frac{1}{5}} + 12005 x^{\frac{1}{5}} + 84035 - 16807$

خطوة 5.2.4.1.9

أضف $- 84035$ و $84035$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 490 x^{\frac{3}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 980 x^{\frac{3}{5}} - 48020 x^{\frac{1}{5}} + 490 x^{\frac{3}{5}} + 72030 x^{\frac{1}{5}} - 48020 x^{\frac{1}{5}} + 12005 x^{\frac{1}{5}} + 0 - 16807$

خطوة 5.2.4.1.10

أضف $x + 490 x^{\frac{3}{5}} + 12005 x^{\frac{1}{5}} + 16807 - 980 x^{\frac{3}{5}} - 48020 x^{\frac{1}{5}} + 490 x^{\frac{3}{5}} + 72030 x^{\frac{1}{5}} - 48020 x^{\frac{1}{5}} + 12005 x^{\frac{1}{5}}$ و $0$ .

خطوة 5.2.4.1.11

اطرح $16807$ من $16807$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 490 x^{\frac{3}{5}} + 12005 x^{\frac{1}{5}} - 980 x^{\frac{3}{5}} - 48020 x^{\frac{1}{5}} + 490 x^{\frac{3}{5}} + 72030 x^{\frac{1}{5}} - 48020 x^{\frac{1}{5}} + 12005 x^{\frac{1}{5}} + 0$

خطوة 5.2.4.1.12

أضف $x + 490 x^{\frac{3}{5}} + 12005 x^{\frac{1}{5}} - 980 x^{\frac{3}{5}} - 48020 x^{\frac{1}{5}} + 490 x^{\frac{3}{5}} + 72030 x^{\frac{1}{5}} - 48020 x^{\frac{1}{5}} + 12005 x^{\frac{1}{5}}$ و $0$ .

خطوة 5.2.4.2

اطرح $980 x^{\frac{3}{5}}$ من $490 x^{\frac{3}{5}}$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 12005 x^{\frac{1}{5}} - 490 x^{\frac{3}{5}} - 48020 x^{\frac{1}{5}} + 490 x^{\frac{3}{5}} + 72030 x^{\frac{1}{5}} - 48020 x^{\frac{1}{5}} + 12005 x^{\frac{1}{5}}$

خطوة 5.2.4.3

جمّع الحدود المتعاكسة في $x + 12005 x^{\frac{1}{5}} - 490 x^{\frac{3}{5}} - 48020 x^{\frac{1}{5}} + 490 x^{\frac{3}{5}} + 72030 x^{\frac{1}{5}} - 48020 x^{\frac{1}{5}} + 12005 x^{\frac{1}{5}}$ .

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خطوة 5.2.4.3.1

أضف $- 490 x^{\frac{3}{5}}$ و $490 x^{\frac{3}{5}}$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 12005 x^{\frac{1}{5}} - 48020 x^{\frac{1}{5}} + 0 + 72030 x^{\frac{1}{5}} - 48020 x^{\frac{1}{5}} + 12005 x^{\frac{1}{5}}$

خطوة 5.2.4.3.2

أضف $x + 12005 x^{\frac{1}{5}} - 48020 x^{\frac{1}{5}}$ و $0$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 12005 x^{\frac{1}{5}} - 48020 x^{\frac{1}{5}} + 72030 x^{\frac{1}{5}} - 48020 x^{\frac{1}{5}} + 12005 x^{\frac{1}{5}}$

خطوة 5.2.4.4

اطرح $48020 x^{\frac{1}{5}}$ من $12005 x^{\frac{1}{5}}$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x - 36015 x^{\frac{1}{5}} + 72030 x^{\frac{1}{5}} - 48020 x^{\frac{1}{5}} + 12005 x^{\frac{1}{5}}$

خطوة 5.2.4.5

أضف $- 36015 x^{\frac{1}{5}}$ و $72030 x^{\frac{1}{5}}$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 36015 x^{\frac{1}{5}} - 48020 x^{\frac{1}{5}} + 12005 x^{\frac{1}{5}}$

خطوة 5.2.4.6

اطرح $48020 x^{\frac{1}{5}}$ من $36015 x^{\frac{1}{5}}$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x - 12005 x^{\frac{1}{5}} + 12005 x^{\frac{1}{5}}$

خطوة 5.2.4.7

جمّع الحدود المتعاكسة في $x - 12005 x^{\frac{1}{5}} + 12005 x^{\frac{1}{5}}$ .

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خطوة 5.2.4.7.1

أضف $- 12005 x^{\frac{1}{5}}$ و $12005 x^{\frac{1}{5}}$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x + 0$

خطوة 5.2.4.7.2

أضف $x$ و $0$ .

$f^{- 1} (7 (x^{\frac{1}{5}} + 7)) = x$

خطوة 5.3

احسِب قيمة $f (f^{- 1} (x))$ .

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خطوة 5.3.1

عيّن دالة النتيجة المركّبة.

$f (f^{- 1} (x))$

خطوة 5.3.2

احسِب قيمة $f (\frac{x^{5}}{16807} - \frac{5 x^{4}}{343} + \frac{10 x^{3}}{7} - 70 x^{2} + 1715 x - 16807)$ باستبدال قيمة $f^{- 1}$ في $f$ .

$f (\frac{x^{5}}{16807} - \frac{5 x^{4}}{343} + \frac{10 x^{3}}{7} - 70 x^{2} + 1715 x - 16807) = 7 ({(\frac{x^{5}}{16807} - \frac{5 x^{4}}{343} + \frac{10 x^{3}}{7} - 70 x^{2} + 1715 x - 16807)}^{\frac{1}{5}} + 7)$

خطوة 5.3.3

طبّق خاصية التوزيع.

$f (\frac{x^{5}}{16807} - \frac{5 x^{4}}{343} + \frac{10 x^{3}}{7} - 70 x^{2} + 1715 x - 16807) = 7 {(\frac{x^{5}}{16807} - \frac{5 x^{4}}{343} + \frac{10 x^{3}}{7} - 70 x^{2} + 1715 x - 16807)}^{\frac{1}{5}} + 7 \cdot 7$

خطوة 5.3.4

اضرب $7$ في $7$ .

خطوة 5.4

بما أن $f^{- 1} (f (x)) = x$ و $f (f^{- 1} (x)) = x$ ، إذن $f^{- 1} (x) = \frac{x^{5}}{16807} - \frac{5 x^{4}}{343} + \frac{10 x^{3}}{7} - 70 x^{2} + 1715 x - 16807$ هي معكوس $f (x) = 7 (x^{\frac{1}{5}} + 7)$ .

$f^{- 1} (x) = \frac{x^{5}}{16807} - \frac{5 x^{4}}{343} + \frac{10 x^{3}}{7} - 70 x^{2} + 1715 x - 16807$