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

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

Evaluate

$$-10a^{2}b^{4}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

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

Use the Commutative Property of Multiplication.

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

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

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

Add the exponents 1 and 1.

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

Add the exponents 2 and 2.

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

Multiply 5 times -2.

$$-10a^{2}b^{4}$$

Differentiate w.r.t. a

$$-20ab^{4}$$