Solve (frac{x^{-4}y^{-5}z^-1}{x^-4y^-4z^-3})

$$( \frac { x ^ { - 4 } y ^ { - 5 } z ^ { - 1 } } { x ^ { - 4 } y ^ { - 4 } z ^ { - 3 } } )$$

Evaluate

$$\frac{z^{2}}{y}$$

Solution Steps

Cancel out x^{-4} in both numerator and denominator.

$$\frac{y^{-5}\times \frac{1}{z}}{y^{-4}z^{-3}}$$

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

$$\frac{y^{-5}z^{2}}{y^{-4}}$$

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

$$\frac{z^{2}}{y^{1}}$$

Calculate y to the power of 1 and get y.

$$\frac{z^{2}}{y}$$

Differentiate w.r.t. y

$$-\left(\frac{z}{y}\right)^{2}$$