Solve 2a^3b^2(-7ab^2)

$$2 a ^ { 3 } b ^ { 2 } ( - 7 a b ^ { 2 } )$$

Evaluate

$$-14\left(ab\right)^{4}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

$$2^{1}a^{3}b^{2}\left(-7\right)^{1}a^{1}b^{2}$$

Use the Commutative Property of Multiplication.

$$2^{1}\left(-7\right)^{1}a^{3}a^{1}b^{2}b^{2}$$

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

$$2^{1}\left(-7\right)^{1}a^{3+1}b^{2+2}$$

Add the exponents 3 and 1.

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

Add the exponents 2 and 2.

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

Multiply 2 times -7.

$$-14a^{4}b^{4}$$

Differentiate w.r.t. a

$$-56a^{3}b^{4}$$