Simplify ( square root of 9x^2y)/(2x^-4y^2)

$\frac{\sqrt{9 x^{2} y}}{2 x^{- 4} y^{2}}$

Move $x^{- 4}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{\sqrt{9 x^{2} y} x^{4}}{2 y^{2}}$

Simplify the numerator.

Rewrite $9 x^{2} y$ as ${(3 x)}^{2} y$ .

Rewrite $9$ as $3^{2}$ .

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

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

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

Pull terms out from under the radical.

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

Multiply $x$ by $x^{4}$ by adding the exponents.

Move $x^{4}$ .

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

Multiply $x^{4}$ by $x$ .

Raise $x$ to the power of $1$ .

$\frac{3 (x^{4} x^{1}) \sqrt{y}}{2 y^{2}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{3 x^{4 + 1} \sqrt{y}}{2 y^{2}}$

Add $4$ and $1$ .

$\frac{3 x^{5} \sqrt{y}}{2 y^{2}}$