Solve (16r^frac{4{19}}s^frac{4{5}})^frac{5{4}}

$$( 16 r ^ { \frac { 4 } { 19 } } s ^ { \frac { 4 } { 5 } } ) ^ { \frac { 5 } { 4 } }$$

Evaluate

$$32\left(|r|\right)^{\frac{5}{19}}|s|$$

Solution Steps

Expand \left(16r^{\frac{4}{19}}s^{\frac{4}{5}}\right)^{\frac{5}{4}}.

$$16^{\frac{5}{4}}\left(r^{\frac{4}{19}}\right)^{\frac{5}{4}}\left(s^{\frac{4}{5}}\right)^{\frac{5}{4}}$$

To raise a power to another power, multiply the exponents. Multiply \frac{4}{19} and \frac{5}{4} to get \frac{5}{19}.

$$16^{\frac{5}{4}}r^{\frac{5}{19}}\left(s^{\frac{4}{5}}\right)^{\frac{5}{4}}$$

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

$$16^{\frac{5}{4}}r^{\frac{5}{19}}s^{1}$$

Calculate 16 to the power of \frac{5}{4} and get 32.

$$32r^{\frac{5}{19}}s^{1}$$

Calculate s to the power of 1 and get s.

$$32r^{\frac{5}{19}}s$$

Differentiate w.r.t. s

$$32\left(|r|\right)^{\frac{5}{19}}sign(s)$$