Solve (16a^8b^4)^frac{3{4}}

$$( 16 a ^ { 8 } b ^ { 4 } ) ^ { \frac { 3 } { 4 } }$$

Evaluate

$$8\left(|b|\right)^{3}a^{6}$$

Solution Steps

Expand \left(16a^{8}b^{4}\right)^{\frac{3}{4}}.

$$16^{\frac{3}{4}}\left(a^{8}\right)^{\frac{3}{4}}\left(b^{4}\right)^{\frac{3}{4}}$$

To raise a power to another power, multiply the exponents. Multiply 8 and \frac{3}{4} to get 6.

$$16^{\frac{3}{4}}a^{6}\left(b^{4}\right)^{\frac{3}{4}}$$

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

$$16^{\frac{3}{4}}a^{6}b^{3}$$

Calculate 16 to the power of \frac{3}{4} and get 8.

$$8a^{6}b^{3}$$

Differentiate w.r.t. b

$$24b|b|a^{6}$$