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

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

Evaluate

$$|y|\left(|x|\right)^{3}$$

Solution Steps

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

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

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

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

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

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

Calculate y to the power of 1 and get y.

$$x^{3}y$$

Differentiate w.r.t. x

$$3x|x||y|$$