Solve (x^-1/3y^6)^1/2

$$( x ^ { - 1 / 3 } y ^ { 6 } ) ^ { 1 / 2 }$$

Evaluate

$$\sqrt{\frac{y^{6}}{\sqrt[3]{x}}}$$

Solution Steps

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

$$\left(x^{-\frac{1}{3}}\right)^{\frac{1}{2}}\left(y^{6}\right)^{\frac{1}{2}}$$

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

$$x^{-\frac{1}{6}}\left(y^{6}\right)^{\frac{1}{2}}$$

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

$$x^{-\frac{1}{6}}y^{3}$$

Differentiate w.r.t. x

$$-\frac{y^{6}}{6x^{\frac{7}{6}}\left(|y|\right)^{3}}$$