Solve 21m^4n^9/14m^7n^2

$$\frac { 21 m ^ { 4 } n ^ { 9 } } { 14 m ^ { 7 } n ^ { 2 } }$$

Evaluate

$$\frac{3n^{7}}{2m^{3}}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{21^{1}m^{4}n^{9}}{14^{1}m^{7}n^{2}}$$

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

$$\frac{21^{1}}{14^{1}}m^{4-7}n^{9-2}$$

Subtract 7 from 4.

$$\frac{21^{1}}{14^{1}}m^{-3}n^{9-2}$$

Subtract 2 from 9.

$$\frac{21^{1}}{14^{1}}\times \frac{1}{m^{3}}n^{7}$$

Reduce the fraction \frac{21}{14} to lowest terms by extracting and canceling out 7.

$$\frac{3}{2}\times \frac{1}{m^{3}}n^{7}$$

Differentiate w.r.t. n

$$\frac{21n^{6}}{2m^{3}}$$