Solve {left(abright)}^frac{1{3}}a^2b^3

$${ \left(ab \right) }^{ \frac{ 1 }{ 3 } } { a }^{ 2 } { b }^{ 3 }$$

Evaluate

$$a^{\frac{7}{3}}b^{\frac{10}{3}}$$

Solution Steps

Expand \left(ab\right)^{\frac{1}{3}}.

$$a^{\frac{1}{3}}b^{\frac{1}{3}}a^{2}b^{3}$$

To multiply powers of the same base, add their exponents. Add \frac{1}{3} and 2 to get \frac{7}{3}.

$$a^{\frac{7}{3}}b^{\frac{1}{3}}b^{3}$$

To multiply powers of the same base, add their exponents. Add \frac{1}{3} and 3 to get \frac{10}{3}.

$$a^{\frac{7}{3}}b^{\frac{10}{3}}$$

Differentiate w.r.t. a

$$\frac{7a^{\frac{4}{3}}b^{\frac{10}{3}}}{3}$$