Evaluate cube root of (128a^9)/(2a^3)

$\sqrt[3]{\frac{128 a^{9}}{2 a^{3}}}$

Step 1

Reduce the expression $\frac{128 a^{9}}{2 a^{3}}$ by cancelling the common factors.

Factor $2$ out of $128 a^{9}$ .

$\sqrt[3]{\frac{2 (64 a^{9})}{2 a^{3}}}$

Factor $2$ out of $2 a^{3}$ .

$\sqrt[3]{\frac{2 (64 a^{9})}{2 (a^{3})}}$

Cancel the common factor.

$\sqrt[3]{\frac{2 (64 a^{9})}{2 a^{3}}}$

Rewrite the expression.

$\sqrt[3]{\frac{64 a^{9}}{a^{3}}}$

Step 2

Cancel the common factor of $a^{9}$ and $a^{3}$ .

Factor $a^{3}$ out of $64 a^{9}$ .

$\sqrt[3]{\frac{a^{3} (64 a^{6})}{a^{3}}}$

Cancel the common factors.

Multiply by $1$ .

$\sqrt[3]{\frac{a^{3} (64 a^{6})}{a^{3} \cdot 1}}$

Cancel the common factor.

$\sqrt[3]{\frac{a^{3} (64 a^{6})}{a^{3} \cdot 1}}$

Rewrite the expression.

$\sqrt[3]{\frac{64 a^{6}}{1}}$

Divide $64 a^{6}$ by $1$ .

$\sqrt[3]{64 a^{6}}$

Step 3

Rewrite $64 a^{6}$ as ${(4 a^{2})}^{3}$ .

$\sqrt[3]{{(4 a^{2})}^{3}}$

Step 4

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

$4 a^{2}$