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

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

Evaluate

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

Solution Steps

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

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

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

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

To raise a power to another power, multiply the exponents. Multiply -\frac{1}{5} and \frac{5}{4} to get -\frac{1}{4}.

$$b^{\frac{5}{2}}c^{-\frac{1}{4}}$$

Differentiate w.r.t. b

$$\frac{5\sqrt[4]{\frac{b^{2}}{\sqrt[5]{c}}}b}{2\sqrt[5]{c}}$$