Write the Fraction in Simplest Form ninth root of 32^3

$\sqrt[9]{32^{3}}$

Step 1

Raise $32$ to the power of $3$ .

$\sqrt[9]{32768}$

Step 2

Rewrite $32768$ as $2^{9} \cdot 64$ .

Factor $512$ out of $32768$ .

$\sqrt[9]{512 (64)}$

Rewrite $512$ as $2^{9}$ .

$\sqrt[9]{2^{9} \cdot 64}$

Step 3

Pull terms out from under the radical.

$2 \sqrt[9]{64}$

Step 4

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

$2 \sqrt[9]{4^{3}}$

Step 5

Rewrite $\sqrt[9]{4^{3}}$ as $\sqrt[3]{\sqrt[3]{4^{3}}}$ .

$2 \sqrt[3]{\sqrt[3]{4^{3}}}$

Step 6

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

$2 \sqrt[3]{4}$