Solve -3m^2n/12m^6n^5

$$\frac { - 3 m ^ { 2 } n } { 12 m ^ { 6 } n ^ { 5 } }$$

Evaluate

$$-\frac{1}{4\left(mn\right)^{4}}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{\left(-3\right)^{1}m^{2}n^{1}}{12^{1}m^{6}n^{5}}$$

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

$$\frac{\left(-3\right)^{1}}{12^{1}}m^{2-6}n^{1-5}$$

Subtract 6 from 2.

$$\frac{\left(-3\right)^{1}}{12^{1}}m^{-4}n^{1-5}$$

Subtract 5 from 1.

$$\frac{\left(-3\right)^{1}}{12^{1}}\times \frac{1}{m^{4}}n^{-4}$$

Reduce the fraction \frac{-3}{12} to lowest terms by extracting and canceling out 3.

$$-\frac{1}{4}\times \frac{1}{m^{4}}\times \frac{1}{n^{4}}$$

Differentiate w.r.t. n

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