Solve -x^-1y^-4/-4x^-4y^-1

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

Evaluate

$$\frac{\left(\frac{x}{y}\right)^{3}}{4}$$

Solution Steps

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

$$\frac{-\frac{1}{x}}{-4x^{-4}y^{3}}$$

Cancel out -1 in both numerator and denominator.

$$\frac{\frac{1}{x}}{4x^{-4}y^{3}}$$

Express \frac{\frac{1}{x}}{4x^{-4}y^{3}} as a single fraction.

$$\frac{1}{x\times 4x^{-4}y^{3}}$$

To multiply powers of the same base, add their exponents. Add 1 and -4 to get -3.

$$\frac{1}{x^{-3}\times 4y^{3}}$$

Differentiate w.r.t. x

$$\frac{3x^{2}}{4y^{3}}$$