Basic Math Examples

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

Step 1

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

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

Step 2

Simplify the numerator.

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Step 2.1

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

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Step 2.1.1

Factor $27$ out of $81$ .

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

Step 2.1.2

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

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

Step 2.2

Pull terms out from under the radical.

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

Step 3

Simplify the denominator.

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Step 3.1

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

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

Step 3.2

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

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

Step 4

Cancel the common factor of $4$ .

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Step 4.1

Cancel the common factor.

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

Step 4.2

Rewrite the expression.

$3 \sqrt[3]{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$3 \sqrt[3]{3}$

Decimal Form:

$4.32674871 \dots$