Solve (x^2y^6)^frac{1{6}}

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

Evaluate

$$\sqrt[3]{|x|}|y|$$

Solution Steps

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

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

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

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

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

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

Calculate y to the power of 1 and get y.

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

Differentiate w.r.t. x

$$\frac{|x||y|}{3x^{\frac{5}{3}}}$$