Simplify cube root of (y^10)/64

$\sqrt[3]{\frac{y^{10}}{64}}$

Step 1

Rewrite $\frac{y^{10}}{64}$ as ${(\frac{y^{3}}{4})}^{3} y$ .

Factor the perfect power ${(y^{3})}^{3}$ out of $y^{10}$ .

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

Factor the perfect power $4^{3}$ out of $64$ .

$\sqrt[3]{\frac{{(y^{3})}^{3} y}{4^{3} \cdot 1}}$

Rearrange the fraction $\frac{{(y^{3})}^{3} y}{4^{3} \cdot 1}$ .

$\sqrt[3]{{(\frac{y^{3}}{4})}^{3} y}$

Step 2

Pull terms out from under the radical.

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

Step 3

Combine $\frac{y^{3}}{4}$ and $\sqrt[3]{y}$ .

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