Solve (-m^2n)(-3m^2)(-5mn^3)=

$$( - m ^ { 2 } n ) ( - 3 m ^ { 2 } ) ( - 5 m n ^ { 3 } ) =$$

Evaluate

$$-15n^{4}m^{5}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

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

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

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

Multiply -3 and -5 to get 15.

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

Multiply -1 and 15 to get -15.

$$-15m^{2}n^{4}m^{3}$$

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

$$-15m^{5}n^{4}$$

Differentiate w.r.t. n

$$-60n^{3}m^{5}$$