Solve frac{(2x^{-4}y^2)^-1}{x^0y^-1}

$$\frac { ( 2 x ^ { - 4 } y ^ { 2 } ) ^ { - 1 } } { x ^ { 0 } y ^ { - 1 } }$$

Evaluate

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

Solution Steps

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

$$\frac{2^{-1}\left(x^{-4}\right)^{-1}\left(y^{2}\right)^{-1}}{x^{0}y^{-1}}$$

To raise a power to another power, multiply the exponents. Multiply -4 and -1 to get 4.

$$\frac{2^{-1}x^{4}\left(y^{2}\right)^{-1}}{x^{0}y^{-1}}$$

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

$$\frac{2^{-1}x^{4}y^{-2}}{x^{0}y^{-1}}$$

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

$$\frac{\frac{1}{2}x^{4}y^{-2}}{x^{0}y^{-1}}$$

Calculate x to the power of 0 and get 1.

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

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

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

Calculate y to the power of 1 and get y.

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

Differentiate w.r.t. x

$$\frac{2x^{3}}{y}$$