Solve (4a^frac{2{3}}b)^frac{1{2}}

$$( 4 a ^ { \frac { 2 } { 3 } } b ) ^ { \frac { 1 } { 2 } }$$

Evaluate

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

Solution Steps

Expand \left(4a^{\frac{2}{3}}b\right)^{\frac{1}{2}}.

$$4^{\frac{1}{2}}\left(a^{\frac{2}{3}}\right)^{\frac{1}{2}}b^{\frac{1}{2}}$$

To raise a power to another power, multiply the exponents. Multiply \frac{2}{3} and \frac{1}{2} to get \frac{1}{3}.

$$4^{\frac{1}{2}}a^{\frac{1}{3}}b^{\frac{1}{2}}$$

Calculate 4 to the power of \frac{1}{2} and get 2.

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

Differentiate w.r.t. a

$$\frac{2\sqrt{b}}{3\sqrt[3]{a|a|}}$$