Solve m^4/n^2*m/n^3

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

Evaluate

$$\left(\frac{m}{n}\right)^{5}$$

Solution Steps

Multiply \frac{m^{4}}{n^{2}} times \frac{m}{n^{3}} by multiplying numerator times numerator and denominator times denominator.

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

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$\frac{m^{5}}{n^{2}n^{3}}$$

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

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

Differentiate w.r.t. m

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