Solve frac{sqrt[3]{x}*sqrt{y^3}}{x^-2/3*y^-1/2}

$$\frac { \sqrt[ 3 ] { x } \cdot \sqrt { y ^ { 3 } } } { x ^ { - 2 / 3 } \cdot y ^ { - 1 / 2 } }$$

Evaluate

$$xy^{2}$$

Short Solution Steps

Factor the expressions that are not already factored.

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

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

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

Expand the expression.

$$\frac{xy^{\frac{3}{2}}}{y^{-\frac{1}{2}}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$xy^{2}$$

Differentiate w.r.t. x

$$y^{2}$$