Solve (r^5s)^frac{3{2}}

$$( r ^ { 5 } s ) ^ { \frac { 3 } { 2 } }$$

Evaluate

$$\left(sr^{5}\right)^{\frac{3}{2}}$$

Solution Steps

Expand \left(r^{5}s\right)^{\frac{3}{2}}.

$$\left(r^{5}\right)^{\frac{3}{2}}s^{\frac{3}{2}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and \frac{3}{2} to get \frac{15}{2}.

$$r^{\frac{15}{2}}s^{\frac{3}{2}}$$

Differentiate w.r.t. r

$$\frac{15s\sqrt{sr^{13}}}{2}$$