Solve (4a^3b^2)(-9ab^5)

$$( 4 a ^ { 3 } b ^ { 2 } ) ( - 9 a b ^ { 5 } )$$

Evaluate

$$-36a^{4}b^{7}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

$$4^{1}a^{3}b^{2}\left(-9\right)^{1}a^{1}b^{5}$$

Use the Commutative Property of Multiplication.

$$4^{1}\left(-9\right)^{1}a^{3}a^{1}b^{2}b^{5}$$

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

$$4^{1}\left(-9\right)^{1}a^{3+1}b^{2+5}$$

Add the exponents 3 and 1.

$$4^{1}\left(-9\right)^{1}a^{4}b^{2+5}$$

Add the exponents 2 and 5.

$$4^{1}\left(-9\right)^{1}a^{4}b^{7}$$

Multiply 4 times -9.

$$-36a^{4}b^{7}$$

Differentiate w.r.t. a

$$-144a^{3}b^{7}$$