Solve (4x^-2/y^4)^-1/2

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

Evaluate

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

Solution Steps

To raise \frac{4x^{-2}}{y^{4}} to a power, raise both numerator and denominator to the power and then divide.

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

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

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

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

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

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

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

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

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

Calculate x to the power of 1 and get x.

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

Differentiate w.r.t. x

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