Solve (a^-6b^1/2)^2/3

$$( a ^ { - 6 } b ^ { 1 / 2 } ) ^ { 2 / 3 }$$

Evaluate

$$\frac{\sqrt[3]{b}}{a^{4}}$$

Solution Steps

Expand \left(a^{-6}b^{\frac{1}{2}}\right)^{\frac{2}{3}}.

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

To raise a power to another power, multiply the exponents. Multiply -6 and \frac{2}{3} to get -4.

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

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

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

Differentiate w.r.t. a

$$-\frac{4\sqrt[3]{b}}{a^{5}}$$