Simplify cube root of (8x^6)/(y^-12)

$\sqrt[3]{\frac{8 x^{6}}{y^{- 12}}}$

Step 1

Move $y^{- 12}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\sqrt[3]{8 x^{6} y^{12}}$

Step 2

Rewrite $8 x^{6} y^{12}$ as ${(2 x^{2} y^{4})}^{3}$ .

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

Step 3

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

$2 x^{2} y^{4}$