Simplify ( square root of 4x^3y^3)/(2x^-1y^3)

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

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

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

Simplify the numerator.

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

Rewrite $4$ as $2^{2}$ .

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

Factor out $x^{2}$ .

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

Factor out $y^{2}$ .

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

Move $x$ .

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

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

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

Add parentheses.

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

Pull terms out from under the radical.

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

Combine exponents.

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

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

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

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

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

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

Add $1$ and $1$ .

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

Reduce the expression by cancelling the common factors.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

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

Factor $y$ out of $x^{2} y \sqrt{x y}$ .

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

Cancel the common factors.

Factor $y$ out of $y^{3}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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