Solve m^-5n^-1/m^2n^-3

$$\frac { m ^ { - 5 } n ^ { - 1 } } { m ^ { 2 } n ^ { - 3 } }$$

Evaluate

$$\frac{n^{2}}{m^{7}}$$

Solution Steps

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

$$\frac{m^{-5}n^{2}}{m^{2}}$$

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

$$\frac{n^{2}}{m^{7}}$$

Differentiate w.r.t. m

$$-\frac{7n^{2}}{m^{8}}$$