Solve 4k^3m^-2n/12km^2n^-5

$$\frac { 4 k ^ { 3 } m ^ { - 2 } n } { 12 k m ^ { 2 } n ^ { - 5 } }$$

Evaluate

$$\frac{k^{2}n^{6}}{3m^{4}}$$

Solution Steps

Cancel out 4k in both numerator and denominator.

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

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

$$\frac{m^{-2}k^{2}n^{6}}{3m^{2}}$$

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

$$\frac{k^{2}n^{6}}{3m^{4}}$$

Differentiate w.r.t. m

$$-\frac{4k^{2}n^{6}}{3m^{5}}$$