Solve (3/4m^4n^2)(-5/3mn)(12/15m^2n^3

$$( \frac { 3 } { 4 } m ^ { 4 } n ^ { 2 } ) ( - \frac { 5 } { 3 } m n ) ( \frac { 12 } { 15 } m ^ { 2 } n ^ { 3 }$$

Evaluate

$$-n^{6}m^{7}$$

Solution Steps

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

$$\frac{3}{4}m^{5}n^{2}\left(-\frac{5}{3}\right)n\times \frac{12}{15}m^{2}n^{3}$$

To multiply powers of the same base, add their exponents. Add 5 and 2 to get 7.

$$\frac{3}{4}m^{7}n^{2}\left(-\frac{5}{3}\right)n\times \frac{12}{15}n^{3}$$

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

$$\frac{3}{4}m^{7}n^{3}\left(-\frac{5}{3}\right)\times \frac{12}{15}n^{3}$$

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

$$\frac{3}{4}m^{7}n^{6}\left(-\frac{5}{3}\right)\times \frac{12}{15}$$

Multiply \frac{3}{4} and -\frac{5}{3} to get -\frac{5}{4}.

$$-\frac{5}{4}m^{7}n^{6}\times \frac{12}{15}$$

Reduce the fraction \frac{12}{15} to lowest terms by extracting and canceling out 3.

$$-\frac{5}{4}m^{7}n^{6}\times \frac{4}{5}$$

Multiply -\frac{5}{4} and \frac{4}{5} to get -1.

$$-m^{7}n^{6}$$

Differentiate w.r.t. m

$$-7\left(mn\right)^{6}$$