Solve (y^frac{1{3}}*z^-frac{2{5}})^4

$$( y ^ { \frac { 1 } { 3 } } \cdot z ^ { - \frac { 2 } { 5 } } ) ^ { 4 }$$

Evaluate

$$\frac{y^{\frac{4}{3}}}{z^{\frac{8}{5}}}$$

Solution Steps

Expand \left(y^{\frac{1}{3}}z^{-\frac{2}{5}}\right)^{4}.

$$\left(y^{\frac{1}{3}}\right)^{4}\left(z^{-\frac{2}{5}}\right)^{4}$$

To raise a power to another power, multiply the exponents. Multiply \frac{1}{3} and 4 to get \frac{4}{3}.

$$y^{\frac{4}{3}}\left(z^{-\frac{2}{5}}\right)^{4}$$

To raise a power to another power, multiply the exponents. Multiply -\frac{2}{5} and 4 to get -\frac{8}{5}.

$$y^{\frac{4}{3}}z^{-\frac{8}{5}}$$

Expand

$$\frac{y^{\frac{4}{3}}}{z^{\frac{8}{5}}}$$

Solution Steps

Expand \left(y^{\frac{1}{3}}z^{-\frac{2}{5}}\right)^{4}.

$$\left(y^{\frac{1}{3}}\right)^{4}\left(z^{-\frac{2}{5}}\right)^{4}$$

To raise a power to another power, multiply the exponents. Multiply \frac{1}{3} and 4 to get \frac{4}{3}.

$$y^{\frac{4}{3}}\left(z^{-\frac{2}{5}}\right)^{4}$$

To raise a power to another power, multiply the exponents. Multiply -\frac{2}{5} and 4 to get -\frac{8}{5}.

$$y^{\frac{4}{3}}z^{-\frac{8}{5}}$$