Solve 35m^8n^5/-7n^2m^6

$$\frac { 35 m ^ { 8 } n ^ { 5 } } { - 7 n ^ { 2 } m ^ { 6 } }$$

Evaluate

$$-5m^{2}n^{3}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{35^{1}m^{8}n^{5}}{\left(-7\right)^{1}m^{6}n^{2}}$$

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

$$\frac{35^{1}}{\left(-7\right)^{1}}m^{8-6}n^{5-2}$$

Subtract 6 from 8.

$$\frac{35^{1}}{\left(-7\right)^{1}}m^{2}n^{5-2}$$

Subtract 2 from 5.

$$\frac{35^{1}}{\left(-7\right)^{1}}m^{2}n^{3}$$

Divide 35 by -7.

$$-5m^{2}n^{3}$$

Differentiate w.r.t. n

$$-15\left(mn\right)^{2}$$