Solve (32a^10b^frac{5{2}})^frac{2{5}}

$$( 32 a ^ { 10 } b ^ { \frac { 5 } { 2 } } ) ^ { \frac { 2 } { 5 } }$$

Evaluate

$$4ba^{4}$$

Solution Steps

Expand \left(32a^{10}b^{\frac{5}{2}}\right)^{\frac{2}{5}}.

$$32^{\frac{2}{5}}\left(a^{10}\right)^{\frac{2}{5}}\left(b^{\frac{5}{2}}\right)^{\frac{2}{5}}$$

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

$$32^{\frac{2}{5}}a^{4}\left(b^{\frac{5}{2}}\right)^{\frac{2}{5}}$$

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

$$32^{\frac{2}{5}}a^{4}b^{1}$$

Calculate 32 to the power of \frac{2}{5} and get 4.

$$4a^{4}b^{1}$$

Calculate b to the power of 1 and get b.

$$4a^{4}b$$

Differentiate w.r.t. b

$$4a^{4}$$