Solve (4*z^2/5*w^-4)^-1/2=

$$( 4 \cdot z ^ { 2 / 5 } \cdot w ^ { - 4 } ) ^ { - 1 / 2 } =$$

Evaluate

$$\frac{w^{2}}{2\sqrt[5]{|z|}}$$

Solution Steps

Expand \left(4z^{\frac{2}{5}}w^{-4}\right)^{-\frac{1}{2}}.

$$4^{-\frac{1}{2}}\left(z^{\frac{2}{5}}\right)^{-\frac{1}{2}}\left(w^{-4}\right)^{-\frac{1}{2}}$$

To raise a power to another power, multiply the exponents. Multiply \frac{2}{5} and -\frac{1}{2} to get -\frac{1}{5}.

$$4^{-\frac{1}{2}}z^{-\frac{1}{5}}\left(w^{-4}\right)^{-\frac{1}{2}}$$

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

$$4^{-\frac{1}{2}}z^{-\frac{1}{5}}w^{2}$$

Calculate 4 to the power of -\frac{1}{2} and get \frac{1}{2}.

$$\frac{1}{2}z^{-\frac{1}{5}}w^{2}$$

Differentiate w.r.t. w

$$\frac{w}{\sqrt[5]{|z|}}$$