Solve 10m^5n^4/2m^2n

$$\frac { 10 m ^ { 5 } n ^ { 4 } } { 2 m ^ { 2 } n }$$

Evaluate

$$5\left(mn\right)^{3}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{10^{1}m^{5}n^{4}}{2^{1}m^{2}n^{1}}$$

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

$$\frac{10^{1}}{2^{1}}m^{5-2}n^{4-1}$$

Subtract 2 from 5.

$$\frac{10^{1}}{2^{1}}m^{3}n^{4-1}$$

Subtract 1 from 4.

$$\frac{10^{1}}{2^{1}}m^{3}n^{3}$$

Divide 10 by 2.

$$5m^{3}n^{3}$$

Differentiate w.r.t. n

$$15n^{2}m^{3}$$