Algebra Examples

$2 m^{10} n^{2} \cdot {(- 7 m^{9} n^{5})}^{2} - {(- m^{7} n^{3})}^{4}$

Step 1

Simplify each term.

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Step 1.1

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 1.1.1

Apply the product rule to $- 7 m^{9} n^{5}$ .

$2 m^{10} n^{2} \cdot ({(- 7 m^{9})}^{2} {(n^{5})}^{2}) - {(- m^{7} n^{3})}^{4}$

Step 1.1.2

Apply the product rule to $- 7 m^{9}$ .

$2 m^{10} n^{2} \cdot ({(- 7)}^{2} {(m^{9})}^{2} {(n^{5})}^{2}) - {(- m^{7} n^{3})}^{4}$

Step 1.2

Raise $- 7$ to the power of $2$ .

$2 m^{10} n^{2} \cdot (49 {(m^{9})}^{2} {(n^{5})}^{2}) - {(- m^{7} n^{3})}^{4}$

Step 1.3

Multiply the exponents in ${(m^{9})}^{2}$ .

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Step 1.3.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$2 m^{10} n^{2} \cdot (49 m^{9 \cdot 2} {(n^{5})}^{2}) - {(- m^{7} n^{3})}^{4}$

Step 1.3.2

Multiply $9$ by $2$ .

$2 m^{10} n^{2} \cdot (49 m^{18} {(n^{5})}^{2}) - {(- m^{7} n^{3})}^{4}$

Step 1.4

Multiply $m^{10}$ by $m^{18}$ by adding the exponents.

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Step 1.4.1

Move $m^{18}$ .

$2 (m^{18} m^{10}) n^{2} \cdot (49 {(n^{5})}^{2}) - {(- m^{7} n^{3})}^{4}$

Step 1.4.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2 m^{18 + 10} n^{2} \cdot (49 {(n^{5})}^{2}) - {(- m^{7} n^{3})}^{4}$

Step 1.4.3

Add $18$ and $10$ .

$2 m^{28} n^{2} \cdot (49 {(n^{5})}^{2}) - {(- m^{7} n^{3})}^{4}$

Step 1.5

Multiply the exponents in ${(n^{5})}^{2}$ .

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Step 1.5.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$2 m^{28} n^{2} \cdot (49 n^{5 \cdot 2}) - {(- m^{7} n^{3})}^{4}$

Step 1.5.2

Multiply $5$ by $2$ .

$2 m^{28} n^{2} \cdot (49 n^{10}) - {(- m^{7} n^{3})}^{4}$

Step 1.6

Multiply $n^{2}$ by $n^{10}$ by adding the exponents.

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Step 1.6.1

Move $n^{10}$ .

$2 m^{28} (n^{10} n^{2}) \cdot 49 - {(- m^{7} n^{3})}^{4}$

Step 1.6.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$2 m^{28} n^{10 + 2} \cdot 49 - {(- m^{7} n^{3})}^{4}$

Step 1.6.3

Add $10$ and $2$ .

$2 m^{28} n^{12} \cdot 49 - {(- m^{7} n^{3})}^{4}$

Step 1.7

Multiply $49$ by $2$ .

$98 m^{28} n^{12} - {(- m^{7} n^{3})}^{4}$

Step 1.8

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 1.8.1

Apply the product rule to $- m^{7} n^{3}$ .

$98 m^{28} n^{12} - ({(- m^{7})}^{4} {(n^{3})}^{4})$

Step 1.8.2

Apply the product rule to $- m^{7}$ .

$98 m^{28} n^{12} - ({(- 1)}^{4} {(m^{7})}^{4} {(n^{3})}^{4})$

Step 1.9

Multiply $- 1$ by ${(- 1)}^{4}$ by adding the exponents.

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Step 1.9.1

Move ${(- 1)}^{4}$ .

$98 m^{28} n^{12} + {(- 1)}^{4} \cdot - 1 ({(m^{7})}^{4} {(n^{3})}^{4})$

Step 1.9.2

Multiply ${(- 1)}^{4}$ by $- 1$ .

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Step 1.9.2.1

Raise $- 1$ to the power of $1$ .

$98 m^{28} n^{12} + {(- 1)}^{4} \cdot {(- 1)}^{1} ({(m^{7})}^{4} {(n^{3})}^{4})$

Step 1.9.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$98 m^{28} n^{12} + {(- 1)}^{4 + 1} ({(m^{7})}^{4} {(n^{3})}^{4})$

Step 1.9.3

Add $4$ and $1$ .

$98 m^{28} n^{12} + {(- 1)}^{5} ({(m^{7})}^{4} {(n^{3})}^{4})$

Step 1.10

Raise $- 1$ to the power of $5$ .

$98 m^{28} n^{12} - ({(m^{7})}^{4} {(n^{3})}^{4})$

Step 1.11

Multiply the exponents in ${(m^{7})}^{4}$ .

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Step 1.11.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$98 m^{28} n^{12} - (m^{7 \cdot 4} {(n^{3})}^{4})$

Step 1.11.2

Multiply $7$ by $4$ .

$98 m^{28} n^{12} - (m^{28} {(n^{3})}^{4})$

Step 1.12

Multiply the exponents in ${(n^{3})}^{4}$ .

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Step 1.12.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$98 m^{28} n^{12} - (m^{28} n^{3 \cdot 4})$

Step 1.12.2

Multiply $3$ by $4$ .

$98 m^{28} n^{12} - (m^{28} n^{12})$

$98 m^{28} n^{12} - m^{28} n^{12}$

Step 2

Subtract $m^{28} n^{12}$ from $98 m^{28} n^{12}$ .

$97 m^{28} n^{12}$