Solve (-4a^5b^7)(-2ab^-2)

$$( - 4 a ^ { 5 } b ^ { 7 } ) ( - 2 a b ^ { - 2 } )$$

Evaluate

$$8b^{5}a^{6}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

$$\left(-4\right)^{1}a^{5}b^{7}\left(-2\right)^{1}a^{1}b^{-2}$$

Use the Commutative Property of Multiplication.

$$\left(-4\right)^{1}\left(-2\right)^{1}a^{5}a^{1}b^{7}b^{-2}$$

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

$$\left(-4\right)^{1}\left(-2\right)^{1}a^{5+1}b^{7-2}$$

Add the exponents 5 and 1.

$$\left(-4\right)^{1}\left(-2\right)^{1}a^{6}b^{7-2}$$

Add the exponents 7 and -2.

$$\left(-4\right)^{1}\left(-2\right)^{1}a^{6}b^{5}$$

Multiply -4 times -2.

$$8a^{6}b^{5}$$

Differentiate w.r.t. a

$$48\left(ab\right)^{5}$$