Solve (x^2y^-8)^frac{1{4}}

$$( x ^ { 2 } y ^ { - 8 } ) ^ { \frac { 1 } { 4 } }$$

Evaluate

$$\frac{\sqrt{|x|}}{y^{2}}$$

Solution Steps

Expand \left(x^{2}y^{-8}\right)^{\frac{1}{4}}.

$$\left(x^{2}\right)^{\frac{1}{4}}\left(y^{-8}\right)^{\frac{1}{4}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and \frac{1}{4} to get \frac{1}{2}.

$$x^{\frac{1}{2}}\left(y^{-8}\right)^{\frac{1}{4}}$$

To raise a power to another power, multiply the exponents. Multiply -8 and \frac{1}{4} to get -2.

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

Differentiate w.r.t. x

$$\frac{sign(x)}{2\sqrt{|x|}y^{2}}$$