Solve (a^3b^9)^2/3

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

Evaluate

$$a^{2}b^{6}$$

Solution Steps

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

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

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

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

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

$$a^{2}b^{6}$$

Differentiate w.r.t. a

$$2ab^{6}$$