Solve (49e^2r^4s^0)^frac{3{2}}

$$( 49 e ^ { 2 } r ^ { 4 } s ^ { 0 } ) ^ { \frac { 3 } { 2 } }$$

Evaluate

$$343e^{3}r^{6}$$

Solution Steps

Calculate s to the power of 0 and get 1.

$$\left(49e^{2}r^{4}\times 1\right)^{\frac{3}{2}}$$

Multiply 49 and 1 to get 49.

$$\left(49e^{2}r^{4}\right)^{\frac{3}{2}}$$

Expand \left(49e^{2}r^{4}\right)^{\frac{3}{2}}.

$$49^{\frac{3}{2}}\left(e^{2}\right)^{\frac{3}{2}}\left(r^{4}\right)^{\frac{3}{2}}$$

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

$$49^{\frac{3}{2}}e^{3}\left(r^{4}\right)^{\frac{3}{2}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and \frac{3}{2} to get 6.

$$49^{\frac{3}{2}}e^{3}r^{6}$$

Calculate 49 to the power of \frac{3}{2} and get 343.

$$343e^{3}r^{6}$$

Differentiate w.r.t. r

$$2058e^{3}r^{5}$$