Basic Math Examples

$4 \sqrt[3]{\frac{81}{64}} + 81 \sqrt[3]{\frac{375}{729}} - 10 \sqrt[3]{\frac{24}{125}}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $\sqrt[3]{\frac{81}{64}}$ as $\frac{\sqrt[3]{81}}{\sqrt[3]{64}}$ .

$4 \frac{\sqrt[3]{81}}{\sqrt[3]{64}} + 81 \sqrt[3]{\frac{375}{729}} - 10 \sqrt[3]{\frac{24}{125}}$

Step 1.2

Simplify the numerator.

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Step 1.2.1

Rewrite $81$ as $3^{3} \cdot 3$ .

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Step 1.2.1.1

Factor $27$ out of $81$ .

$4 \frac{\sqrt[3]{27 (3)}}{\sqrt[3]{64}} + 81 \sqrt[3]{\frac{375}{729}} - 10 \sqrt[3]{\frac{24}{125}}$

Step 1.2.1.2

Rewrite $27$ as $3^{3}$ .

$4 \frac{\sqrt[3]{3^{3} \cdot 3}}{\sqrt[3]{64}} + 81 \sqrt[3]{\frac{375}{729}} - 10 \sqrt[3]{\frac{24}{125}}$

Step 1.2.2

Pull terms out from under the radical.

$4 \frac{3 \sqrt[3]{3}}{\sqrt[3]{64}} + 81 \sqrt[3]{\frac{375}{729}} - 10 \sqrt[3]{\frac{24}{125}}$

Step 1.3

Simplify the denominator.

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Step 1.3.1

Rewrite $64$ as $4^{3}$ .

$4 \frac{3 \sqrt[3]{3}}{\sqrt[3]{4^{3}}} + 81 \sqrt[3]{\frac{375}{729}} - 10 \sqrt[3]{\frac{24}{125}}$

Step 1.3.2

Pull terms out from under the radical, assuming real numbers.

$4 \frac{3 \sqrt[3]{3}}{4} + 81 \sqrt[3]{\frac{375}{729}} - 10 \sqrt[3]{\frac{24}{125}}$

Step 1.4

Cancel the common factor of $4$ .

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Step 1.4.1

Cancel the common factor.

$4 \frac{3 \sqrt[3]{3}}{4} + 81 \sqrt[3]{\frac{375}{729}} - 10 \sqrt[3]{\frac{24}{125}}$

Step 1.4.2

Rewrite the expression.

$3 \sqrt[3]{3} + 81 \sqrt[3]{\frac{375}{729}} - 10 \sqrt[3]{\frac{24}{125}}$

Step 1.5

Cancel the common factor of $375$ and $729$ .

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Step 1.5.1

Factor $3$ out of $375$ .

$3 \sqrt[3]{3} + 81 \sqrt[3]{\frac{3 (125)}{729}} - 10 \sqrt[3]{\frac{24}{125}}$

Step 1.5.2

Cancel the common factors.

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Step 1.5.2.1

Factor $3$ out of $729$ .

$3 \sqrt[3]{3} + 81 \sqrt[3]{\frac{3 \cdot 125}{3 \cdot 243}} - 10 \sqrt[3]{\frac{24}{125}}$

Step 1.5.2.2

Cancel the common factor.

$3 \sqrt[3]{3} + 81 \sqrt[3]{\frac{3 \cdot 125}{3 \cdot 243}} - 10 \sqrt[3]{\frac{24}{125}}$

Step 1.5.2.3

Rewrite the expression.

$3 \sqrt[3]{3} + 81 \sqrt[3]{\frac{125}{243}} - 10 \sqrt[3]{\frac{24}{125}}$

Step 1.6

Rewrite $\sqrt[3]{\frac{125}{243}}$ as $\frac{\sqrt[3]{125}}{\sqrt[3]{243}}$ .

$3 \sqrt[3]{3} + 81 \frac{\sqrt[3]{125}}{\sqrt[3]{243}} - 10 \sqrt[3]{\frac{24}{125}}$

Step 1.7

Simplify the numerator.

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Step 1.7.1

Rewrite $125$ as $5^{3}$ .

$3 \sqrt[3]{3} + 81 \frac{\sqrt[3]{5^{3}}}{\sqrt[3]{243}} - 10 \sqrt[3]{\frac{24}{125}}$

Step 1.7.2

Pull terms out from under the radical, assuming real numbers.

$3 \sqrt[3]{3} + 81 \frac{5}{\sqrt[3]{243}} - 10 \sqrt[3]{\frac{24}{125}}$

Step 1.8

Simplify the denominator.

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Step 1.8.1

Rewrite $243$ as $3^{3} \cdot 9$ .

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Step 1.8.1.1

Factor $27$ out of $243$ .

$3 \sqrt[3]{3} + 81 \frac{5}{\sqrt[3]{27 (9)}} - 10 \sqrt[3]{\frac{24}{125}}$

Step 1.8.1.2

Rewrite $27$ as $3^{3}$ .

$3 \sqrt[3]{3} + 81 \frac{5}{\sqrt[3]{3^{3} \cdot 9}} - 10 \sqrt[3]{\frac{24}{125}}$

Step 1.8.2

Pull terms out from under the radical.

$3 \sqrt[3]{3} + 81 \frac{5}{3 \sqrt[3]{9}} - 10 \sqrt[3]{\frac{24}{125}}$

Step 1.9

Cancel the common factor of $3$ .

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Step 1.9.1

Factor $3$ out of $81$ .

$3 \sqrt[3]{3} + 3 (27) \frac{5}{3 \sqrt[3]{9}} - 10 \sqrt[3]{\frac{24}{125}}$

Step 1.9.2

Factor $3$ out of $3 \sqrt[3]{9}$ .

$3 \sqrt[3]{3} + 3 (27) \frac{5}{3 (\sqrt[3]{9})} - 10 \sqrt[3]{\frac{24}{125}}$

Step 1.9.3

Cancel the common factor.

$3 \sqrt[3]{3} + 3 \cdot 27 \frac{5}{3 \sqrt[3]{9}} - 10 \sqrt[3]{\frac{24}{125}}$

Step 1.9.4

Rewrite the expression.

$3 \sqrt[3]{3} + 27 \frac{5}{\sqrt[3]{9}} - 10 \sqrt[3]{\frac{24}{125}}$

Step 1.10

Combine $27$ and $\frac{5}{\sqrt[3]{9}}$ .

$3 \sqrt[3]{3} + \frac{27 \cdot 5}{\sqrt[3]{9}} - 10 \sqrt[3]{\frac{24}{125}}$

Step 1.11

Multiply $27$ by $5$ .

$3 \sqrt[3]{3} + \frac{135}{\sqrt[3]{9}} - 10 \sqrt[3]{\frac{24}{125}}$

Step 1.12

Multiply $\frac{135}{\sqrt[3]{9}}$ by $\frac{{\sqrt[3]{9}}^{2}}{{\sqrt[3]{9}}^{2}}$ .

$3 \sqrt[3]{3} + \frac{135}{\sqrt[3]{9}} \cdot \frac{{\sqrt[3]{9}}^{2}}{{\sqrt[3]{9}}^{2}} - 10 \sqrt[3]{\frac{24}{125}}$

Step 1.13

Combine and simplify the denominator.

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Step 1.13.1

Multiply $\frac{135}{\sqrt[3]{9}}$ by $\frac{{\sqrt[3]{9}}^{2}}{{\sqrt[3]{9}}^{2}}$ .

$3 \sqrt[3]{3} + \frac{135 {\sqrt[3]{9}}^{2}}{\sqrt[3]{9} {\sqrt[3]{9}}^{2}} - 10 \sqrt[3]{\frac{24}{125}}$

Step 1.13.2

Raise $\sqrt[3]{9}$ to the power of $1$ .

$3 \sqrt[3]{3} + \frac{135 {\sqrt[3]{9}}^{2}}{{\sqrt[3]{9}}^{1} {\sqrt[3]{9}}^{2}} - 10 \sqrt[3]{\frac{24}{125}}$

Step 1.13.3

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

$3 \sqrt[3]{3} + \frac{135 {\sqrt[3]{9}}^{2}}{{\sqrt[3]{9}}^{1 + 2}} - 10 \sqrt[3]{\frac{24}{125}}$

Step 1.13.4

Add $1$ and $2$ .

$3 \sqrt[3]{3} + \frac{135 {\sqrt[3]{9}}^{2}}{{\sqrt[3]{9}}^{3}} - 10 \sqrt[3]{\frac{24}{125}}$

Step 1.13.5

Rewrite ${\sqrt[3]{9}}^{3}$ as $9$ .

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Step 1.13.5.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{9}$ as $9^{\frac{1}{3}}$ .

$3 \sqrt[3]{3} + \frac{135 {\sqrt[3]{9}}^{2}}{{(9^{\frac{1}{3}})}^{3}} - 10 \sqrt[3]{\frac{24}{125}}$

Step 1.13.5.2

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

$3 \sqrt[3]{3} + \frac{135 {\sqrt[3]{9}}^{2}}{9^{\frac{1}{3} \cdot 3}} - 10 \sqrt[3]{\frac{24}{125}}$

Step 1.13.5.3

Combine $\frac{1}{3}$ and $3$ .

$3 \sqrt[3]{3} + \frac{135 {\sqrt[3]{9}}^{2}}{9^{\frac{3}{3}}} - 10 \sqrt[3]{\frac{24}{125}}$

Step 1.13.5.4

Cancel the common factor of $3$ .

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Step 1.13.5.4.1

Cancel the common factor.

$3 \sqrt[3]{3} + \frac{135 {\sqrt[3]{9}}^{2}}{9^{\frac{3}{3}}} - 10 \sqrt[3]{\frac{24}{125}}$

Step 1.13.5.4.2

Rewrite the expression.

$3 \sqrt[3]{3} + \frac{135 {\sqrt[3]{9}}^{2}}{9^{1}} - 10 \sqrt[3]{\frac{24}{125}}$

Step 1.13.5.5

Evaluate the exponent.

$3 \sqrt[3]{3} + \frac{135 {\sqrt[3]{9}}^{2}}{9} - 10 \sqrt[3]{\frac{24}{125}}$

Step 1.14

Cancel the common factor of $135$ and $9$ .

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Step 1.14.1

Factor $9$ out of $135 {\sqrt[3]{9}}^{2}$ .

$3 \sqrt[3]{3} + \frac{9 (15 {\sqrt[3]{9}}^{2})}{9} - 10 \sqrt[3]{\frac{24}{125}}$

Step 1.14.2

Cancel the common factors.

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Step 1.14.2.1

Factor $9$ out of $9$ .

$3 \sqrt[3]{3} + \frac{9 (15 {\sqrt[3]{9}}^{2})}{9 (1)} - 10 \sqrt[3]{\frac{24}{125}}$

Step 1.14.2.2

Cancel the common factor.

$3 \sqrt[3]{3} + \frac{9 (15 {\sqrt[3]{9}}^{2})}{9 \cdot 1} - 10 \sqrt[3]{\frac{24}{125}}$

Step 1.14.2.3

Rewrite the expression.

$3 \sqrt[3]{3} + \frac{15 {\sqrt[3]{9}}^{2}}{1} - 10 \sqrt[3]{\frac{24}{125}}$

Step 1.14.2.4

Divide $15 {\sqrt[3]{9}}^{2}$ by $1$ .

$3 \sqrt[3]{3} + 15 {\sqrt[3]{9}}^{2} - 10 \sqrt[3]{\frac{24}{125}}$

Step 1.15

Rewrite ${\sqrt[3]{9}}^{2}$ as $\sqrt[3]{9^{2}}$ .

$3 \sqrt[3]{3} + 15 \sqrt[3]{9^{2}} - 10 \sqrt[3]{\frac{24}{125}}$

Step 1.16

Raise $9$ to the power of $2$ .

$3 \sqrt[3]{3} + 15 \sqrt[3]{81} - 10 \sqrt[3]{\frac{24}{125}}$

Step 1.17

Rewrite $81$ as $3^{3} \cdot 3$ .

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Step 1.17.1

Factor $27$ out of $81$ .

$3 \sqrt[3]{3} + 15 \sqrt[3]{27 (3)} - 10 \sqrt[3]{\frac{24}{125}}$

Step 1.17.2

Rewrite $27$ as $3^{3}$ .

$3 \sqrt[3]{3} + 15 \sqrt[3]{3^{3} \cdot 3} - 10 \sqrt[3]{\frac{24}{125}}$

Step 1.18

Pull terms out from under the radical.

$3 \sqrt[3]{3} + 15 (3 \sqrt[3]{3}) - 10 \sqrt[3]{\frac{24}{125}}$

Step 1.19

Multiply $3$ by $15$ .

$3 \sqrt[3]{3} + 45 \sqrt[3]{3} - 10 \sqrt[3]{\frac{24}{125}}$

Step 1.20

Rewrite $\sqrt[3]{\frac{24}{125}}$ as $\frac{\sqrt[3]{24}}{\sqrt[3]{125}}$ .

$3 \sqrt[3]{3} + 45 \sqrt[3]{3} - 10 \frac{\sqrt[3]{24}}{\sqrt[3]{125}}$

Step 1.21

Simplify the numerator.

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Step 1.21.1

Rewrite $24$ as $2^{3} \cdot 3$ .

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Step 1.21.1.1

Factor $8$ out of $24$ .

$3 \sqrt[3]{3} + 45 \sqrt[3]{3} - 10 \frac{\sqrt[3]{8 (3)}}{\sqrt[3]{125}}$

Step 1.21.1.2

Rewrite $8$ as $2^{3}$ .

$3 \sqrt[3]{3} + 45 \sqrt[3]{3} - 10 \frac{\sqrt[3]{2^{3} \cdot 3}}{\sqrt[3]{125}}$

Step 1.21.2

Pull terms out from under the radical.

$3 \sqrt[3]{3} + 45 \sqrt[3]{3} - 10 \frac{2 \sqrt[3]{3}}{\sqrt[3]{125}}$

Step 1.22

Simplify the denominator.

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Step 1.22.1

Rewrite $125$ as $5^{3}$ .

$3 \sqrt[3]{3} + 45 \sqrt[3]{3} - 10 \frac{2 \sqrt[3]{3}}{\sqrt[3]{5^{3}}}$

Step 1.22.2

Pull terms out from under the radical, assuming real numbers.

$3 \sqrt[3]{3} + 45 \sqrt[3]{3} - 10 \frac{2 \sqrt[3]{3}}{5}$

Step 1.23

Cancel the common factor of $5$ .

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Step 1.23.1

Factor $5$ out of $- 10$ .

$3 \sqrt[3]{3} + 45 \sqrt[3]{3} + 5 (- 2) \frac{2 \sqrt[3]{3}}{5}$

Step 1.23.2

Cancel the common factor.

$3 \sqrt[3]{3} + 45 \sqrt[3]{3} + 5 \cdot - 2 \frac{2 \sqrt[3]{3}}{5}$

Step 1.23.3

Rewrite the expression.

$3 \sqrt[3]{3} + 45 \sqrt[3]{3} - 2 (2 \sqrt[3]{3})$

Step 1.24

Multiply $2$ by $- 2$ .

$3 \sqrt[3]{3} + 45 \sqrt[3]{3} - 4 \sqrt[3]{3}$

Step 2

Simplify by adding terms.

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Step 2.1

Add $3 \sqrt[3]{3}$ and $45 \sqrt[3]{3}$ .

$48 \sqrt[3]{3} - 4 \sqrt[3]{3}$

Step 2.2

Subtract $4 \sqrt[3]{3}$ from $48 \sqrt[3]{3}$ .

$44 \sqrt[3]{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$44 \sqrt[3]{3}$

Decimal Form:

$63.45898109 \dots$