Solve (b^-frac{1{5}}*a^4)^frac{5{2}}

$$( b ^ { - \frac { 1 } { 5 } } \cdot a ^ { 4 } ) ^ { \frac { 5 } { 2 } }$$

Evaluate

$$\left(\frac{a^{4}}{\sqrt[5]{b}}\right)^{\frac{5}{2}}$$

Solution Steps

Expand \left(b^{-\frac{1}{5}}a^{4}\right)^{\frac{5}{2}}.

$$\left(b^{-\frac{1}{5}}\right)^{\frac{5}{2}}\left(a^{4}\right)^{\frac{5}{2}}$$

To raise a power to another power, multiply the exponents. Multiply -\frac{1}{5} and \frac{5}{2} to get -\frac{1}{2}.

$$b^{-\frac{1}{2}}\left(a^{4}\right)^{\frac{5}{2}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and \frac{5}{2} to get 10.

$$b^{-\frac{1}{2}}a^{10}$$

Differentiate w.r.t. b

$$-\frac{\left(\frac{a^{\frac{20}{3}}}{b}\right)^{\frac{3}{2}}}{2}$$