Solve x^-9y^3/x^3y^-2

$$\frac{ { x }^{ -9 } { y }^{ 3 } }{ { x }^{ 3 } { y }^{ -2 } }$$

Evaluate

$$\frac{y^{5}}{x^{12}}$$

Solution Steps

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

$$\frac{x^{-9}y^{5}}{x^{3}}$$

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

$$\frac{y^{5}}{x^{12}}$$

Differentiate w.r.t. x

$$-\frac{12y^{5}}{x^{13}}$$