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

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

Evaluate

$$\sqrt[3]{|a|}b^{\frac{3}{8}}$$

Solution Steps

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

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

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

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

To raise a power to another power, multiply the exponents. Multiply \frac{3}{4} and \frac{1}{2} to get \frac{3}{8}.

$$a^{\frac{1}{3}}b^{\frac{3}{8}}$$

Differentiate w.r.t. a

$$\frac{b^{\frac{3}{8}}|a|}{3a^{\frac{5}{3}}}$$