Solve a^mb^2*(-3a^3b^nc)=

$$a ^ { m } b ^ { 2 } \cdot ( - 3 a ^ { 3 } b ^ { n } c ) =$$

Evaluate

$$-3ca^{m+3}b^{n+2}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

$$\left(-3\right)^{1}a^{m}b^{2}c^{1}a^{3}b^{n}$$

Use the Commutative Property of Multiplication.

$$\left(-3\right)^{1}c^{1}a^{m}a^{3}b^{2}b^{n}$$

To multiply powers of the same base, add their exponents.

$$\left(-3\right)^{1}c^{1}a^{m+3}b^{2+n}$$

Add the exponents 2 and n.

$$\left(-3\right)^{1}c^{1}a^{m+3}b^{n+2}$$

Multiply -3 times c.

$$\left(-3c\right)a^{m+3}b^{n+2}$$

Differentiate w.r.t. b

$$-3c\left(n+2\right)a^{m+3}b^{n+1}$$