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

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

Evaluate

$$\frac{\sqrt{z}}{x^{\frac{10}{3}}}$$

Solution Steps

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

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

To raise a power to another power, multiply the exponents. Multiply \frac{1}{4} and 2 to get \frac{1}{2}.

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

To raise a power to another power, multiply the exponents. Multiply -\frac{5}{3} and 2 to get -\frac{10}{3}.

$$z^{\frac{1}{2}}x^{-\frac{10}{3}}$$

Expand

$$\frac{\sqrt{z}}{x^{\frac{10}{3}}}$$

Solution Steps

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

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

To raise a power to another power, multiply the exponents. Multiply \frac{1}{4} and 2 to get \frac{1}{2}.

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

To raise a power to another power, multiply the exponents. Multiply -\frac{5}{3} and 2 to get -\frac{10}{3}.

$$z^{\frac{1}{2}}x^{-\frac{10}{3}}$$