Solve frac{y^{-2}z^-5}{y^2z^-6})^-2a

$$\frac { y ^ { - 2 } z ^ { - 5 } } { y ^ { 2 } z ^ { - 6 } } ) ^ { - 2 } a$$

Evaluate

$$\frac{z}{y^{4}}$$

Solution Steps

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

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

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

$$\frac{z^{1}}{y^{4}}$$

Calculate z to the power of 1 and get z.

$$\frac{z}{y^{4}}$$

Differentiate w.r.t. y

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