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

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

Evaluate

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

Solution Steps

To raise \frac{x^{6}}{y^{2}} to a power, raise both numerator and denominator to the power and then divide.

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

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

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

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

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

Calculate y to the power of 1 and get y.

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

Differentiate w.r.t. x

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