Algebra Examples

\sqrt[3]{\frac{27}{64}}

$\sqrt[3]{\frac{27}{64}}$

Step 1

Rewrite

\sqrt[3]{\frac{27}{64}}

$\sqrt[3]{\frac{27}{64}}$ as

\frac{\sqrt[3]{27}}{\sqrt[3]{64}}

$\frac{\sqrt[3]{27}}{\sqrt[3]{64}}$ .

\frac{\sqrt[3]{27}}{\sqrt[3]{64}}

$\frac{\sqrt[3]{27}}{\sqrt[3]{64}}$

Step 2

Simplify the numerator.

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Step 2.1

Rewrite

27

$27$ as

3^{3}

$3^{3}$ .

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

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

Step 2.2

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

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

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

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

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

Step 3

Simplify the denominator.

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Step 3.1

Rewrite

64

$64$ as

4^{3}

$4^{3}$ .

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

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

Step 3.2

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

\frac{3}{4}

$\frac{3}{4}$

\frac{3}{4}

$\frac{3}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

\frac{3}{4}

$\frac{3}{4}$

Decimal Form:

0.75

$0.75$

\sqrt[3]{\frac{27}{64}}

$\sqrt[3]{\frac{27}{64}}$

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