Solve {left(x^2y^-1right)}^-frac{1{2}}

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

Evaluate

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

Solution Steps

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

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

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

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

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

$$x^{-1}y^{\frac{1}{2}}$$

Differentiate w.r.t. x

$$-\frac{\sqrt{y}|x|}{x^{3}}$$