Basic Math Examples

4 \sqrt[3]{\frac{81}{64}}

$4 \sqrt[3]{\frac{81}{64}}$

Step 1

Rewrite

\sqrt[3]{\frac{81}{64}}

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

\frac{\sqrt[3]{81}}{\sqrt[3]{64}}

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

4 \frac{\sqrt[3]{81}}{\sqrt[3]{64}}

$4 \frac{\sqrt[3]{81}}{\sqrt[3]{64}}$

Step 2

Simplify the numerator.

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Step 2.1

Rewrite

81

$81$ as

3^{3} \cdot 3

$3^{3} \cdot 3$ .

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Step 2.1.1

Factor

27

$27$ out of

81

$81$ .

4 \frac{\sqrt[3]{27 (3)}}{\sqrt[3]{64}}

$4 \frac{\sqrt[3]{27 (3)}}{\sqrt[3]{64}}$

Step 2.1.2

Rewrite

27

$27$ as

3^{3}

$3^{3}$ .

4 \frac{\sqrt[3]{3^{3} \cdot 3}}{\sqrt[3]{64}}

$4 \frac{\sqrt[3]{3^{3} \cdot 3}}{\sqrt[3]{64}}$

4 \frac{\sqrt[3]{3^{3} \cdot 3}}{\sqrt[3]{64}}

$4 \frac{\sqrt[3]{3^{3} \cdot 3}}{\sqrt[3]{64}}$

Step 2.2

Pull terms out from under the radical.

4 \frac{3 \sqrt[3]{3}}{\sqrt[3]{64}}

$4 \frac{3 \sqrt[3]{3}}{\sqrt[3]{64}}$

4 \frac{3 \sqrt[3]{3}}{\sqrt[3]{64}}

$4 \frac{3 \sqrt[3]{3}}{\sqrt[3]{64}}$

Step 3

Simplify the denominator.

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Step 3.1

Rewrite

64

$64$ as

4^{3}

$4^{3}$ .

4 \frac{3 \sqrt[3]{3}}{\sqrt[3]{4^{3}}}

$4 \frac{3 \sqrt[3]{3}}{\sqrt[3]{4^{3}}}$

Step 3.2

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

4 \frac{3 \sqrt[3]{3}}{4}

$4 \frac{3 \sqrt[3]{3}}{4}$

4 \frac{3 \sqrt[3]{3}}{4}

$4 \frac{3 \sqrt[3]{3}}{4}$

Step 4

Cancel the common factor of

4

$4$ .

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Step 4.1

Cancel the common factor.

$4 \frac{3 \sqrt[3]{3}}{4}$

Step 4.2

Rewrite the expression.

$3 \sqrt[3]{3}$

$3 \sqrt[3]{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$3 \sqrt[3]{3}$

Decimal Form:

$4.32674871 \dots$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$