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

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

Evaluate

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

Solution Steps

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

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

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

$$a^{\frac{1}{8}}\left(b^{-1}\right)^{\frac{1}{2}}$$

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

$$a^{\frac{1}{8}}b^{-\frac{1}{2}}$$

Differentiate w.r.t. a

$$\frac{1}{8\sqrt{\frac{\sqrt[4]{a}}{b}}a^{\frac{3}{4}}b}$$