Solve (a^2b)^frac{1{6}}*a^frac{1{3}}

$$( a ^ { 2 } b ) ^ { \frac { 1 } { 6 } } \times a ^ { \frac { 1 } { 3 } }$$

Evaluate

$$\sqrt[3]{a}\sqrt[6]{ba^{2}}$$

Solution Steps

Expand \left(a^{2}b\right)^{\frac{1}{6}}.

$$\left(a^{2}\right)^{\frac{1}{6}}b^{\frac{1}{6}}a^{\frac{1}{3}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and \frac{1}{6} to get \frac{1}{3}.

$$a^{\frac{1}{3}}b^{\frac{1}{6}}a^{\frac{1}{3}}$$

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

$$a^{\frac{2}{3}}b^{\frac{1}{6}}$$

Differentiate w.r.t. a

$$\frac{2\sqrt[6]{b}}{3\sqrt[3]{|a|}}$$