Solve (125a^9b^-6)^2/3

$$( 125 a ^ { 9 } b ^ { - 6 } ) ^ { 2 / 3 }$$

Evaluate

$$\frac{25a^{6}}{b^{4}}$$

Solution Steps

Expand \left(125a^{9}b^{-6}\right)^{\frac{2}{3}}.

$$125^{\frac{2}{3}}\left(a^{9}\right)^{\frac{2}{3}}\left(b^{-6}\right)^{\frac{2}{3}}$$

To raise a power to another power, multiply the exponents. Multiply 9 and \frac{2}{3} to get 6.

$$125^{\frac{2}{3}}a^{6}\left(b^{-6}\right)^{\frac{2}{3}}$$

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

$$125^{\frac{2}{3}}a^{6}b^{-4}$$

Calculate 125 to the power of \frac{2}{3} and get 25.

$$25a^{6}b^{-4}$$

Differentiate w.r.t. a

$$\frac{150a^{5}}{b^{4}}$$