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

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

Evaluate

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

Solution Steps

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

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

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

$$x^{4}\left(y^{-\frac{1}{6}}\right)^{6}$$

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

$$x^{4}y^{-1}$$

Expand

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

Solution Steps

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

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

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

$$x^{4}\left(y^{-\frac{1}{6}}\right)^{6}$$

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

$$x^{4}y^{-1}$$