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

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

Evaluate

$$-10\left(ab\right)^{3}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

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

Use the Commutative Property of Multiplication.

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

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

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

Add the exponents 1 and 2.

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

Add the exponents 2 and 1.

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

Multiply 5 times -2.

$$-10a^{3}b^{3}$$

Differentiate w.r.t. a

$$-30a^{2}b^{3}$$