Solve 16m^8n/12m^5n^3

$$\frac { 16 m ^ { 8 } n } { 12 m ^ { 5 } n ^ { 3 } }$$

Evaluate

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

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{16^{1}m^{8}n^{1}}{12^{1}m^{5}n^{3}}$$

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

$$\frac{16^{1}}{12^{1}}m^{8-5}n^{1-3}$$

Subtract 5 from 8.

$$\frac{16^{1}}{12^{1}}m^{3}n^{1-3}$$

Subtract 3 from 1.

$$\frac{16^{1}}{12^{1}}m^{3}n^{-2}$$

Reduce the fraction \frac{16}{12} to lowest terms by extracting and canceling out 4.

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

Differentiate w.r.t. n

$$-\frac{8\times \left(\frac{m}{n}\right)^{3}}{3}$$