Solve 27m^6n^9/6m^3n^1

$$\frac { 27 m ^ { 6 } n ^ { 9 } } { 6 m ^ { 3 } n ^ { 1 } }$$

Evaluate

$$\frac{9m^{3}n^{8}}{2}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{27^{1}m^{6}n^{9}}{6^{1}m^{3}n^{1}}$$

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

$$\frac{27^{1}}{6^{1}}m^{6-3}n^{9-1}$$

Subtract 3 from 6.

$$\frac{27^{1}}{6^{1}}m^{3}n^{9-1}$$

Subtract 1 from 9.

$$\frac{27^{1}}{6^{1}}m^{3}n^{8}$$

Reduce the fraction \frac{27}{6} to lowest terms by extracting and canceling out 3.

$$\frac{9}{2}m^{3}n^{8}$$

Differentiate w.r.t. n

$$36m^{3}n^{7}$$