Solve (x^frac{1{2}}y^-frac{2{3}})^-6

$$( x ^ { \frac { 1 } { 2 } } y ^ { - \frac { 2 } { 3 } } ) ^ { - 6 }$$

Evaluate

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

Solution Steps

Expand \left(x^{\frac{1}{2}}y^{-\frac{2}{3}}\right)^{-6}.

$$\left(x^{\frac{1}{2}}\right)^{-6}\left(y^{-\frac{2}{3}}\right)^{-6}$$

To raise a power to another power, multiply the exponents. Multiply \frac{1}{2} and -6 to get -3.

$$x^{-3}\left(y^{-\frac{2}{3}}\right)^{-6}$$

To raise a power to another power, multiply the exponents. Multiply -\frac{2}{3} and -6 to get 4.

$$x^{-3}y^{4}$$

Expand

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

Solution Steps

Expand \left(x^{\frac{1}{2}}y^{-\frac{2}{3}}\right)^{-6}.

$$\left(x^{\frac{1}{2}}\right)^{-6}\left(y^{-\frac{2}{3}}\right)^{-6}$$

To raise a power to another power, multiply the exponents. Multiply \frac{1}{2} and -6 to get -3.

$$x^{-3}\left(y^{-\frac{2}{3}}\right)^{-6}$$

To raise a power to another power, multiply the exponents. Multiply -\frac{2}{3} and -6 to get 4.

$$x^{-3}y^{4}$$