Simplify ( fourth root of 81x^2y)/(2x^-1y)

$\frac{\sqrt[4]{81 x^{2} y}}{2 x^{- 1} y}$

Step 1

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

$\frac{\sqrt[4]{81 x^{2} y} x}{2 y}$

Step 2

Simplify the numerator.

Rewrite $81 x^{2} y$ as $3^{4} (x^{2} y)$ .

Rewrite $81$ as $3^{4}$ .

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

Add parentheses.

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

Pull terms out from under the radical.

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