Solve m^2n^2s^2:13mns

$$m ^ { 2 } n ^ { 2 } s ^ { 2 } : 13 m n s$$

Evaluate

$$\frac{\left(mns\right)^{3}}{13}$$

Solution Steps

Express \frac{m^{2}n^{2}s^{2}}{13}m as a single fraction.

$$\frac{m^{2}n^{2}s^{2}m}{13}ns$$

Express \frac{m^{2}n^{2}s^{2}m}{13}n as a single fraction.

$$\frac{m^{2}n^{2}s^{2}mn}{13}s$$

Express \frac{m^{2}n^{2}s^{2}mn}{13}s as a single fraction.

$$\frac{m^{2}n^{2}s^{2}mns}{13}$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{m^{3}n^{2}s^{2}ns}{13}$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{m^{3}n^{3}s^{2}s}{13}$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{m^{3}n^{3}s^{3}}{13}$$

Differentiate w.r.t. m

$$\frac{3m^{2}\left(ns\right)^{3}}{13}$$