Simplify cube root of 64/27

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

Step 1

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

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

Step 2

Simplify the numerator.

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

$\frac{\sqrt[3]{4^{3}}}{\sqrt[3]{27}}$

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

$\frac{4}{\sqrt[3]{27}}$

Step 3

Simplify the denominator.

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

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

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

$\frac{4}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{4}{3}$

Decimal Form:

$1.\overline{3}$

Mixed Number Form:

$1 \frac{1}{3}$