Solve (7a^3b^3)(2a^-4b)

$$( 7 a ^ { 3 } b ^ { 3 } ) ( 2 a ^ { - 4 } b )$$

Evaluate

$$\frac{14b^{4}}{a}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

$$7^{1}a^{3}b^{3}\times 2^{1}a^{-4}b^{1}$$

Use the Commutative Property of Multiplication.

$$7^{1}\times 2^{1}a^{3}a^{-4}b^{3}b^{1}$$

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

$$7^{1}\times 2^{1}a^{3-4}b^{3+1}$$

Add the exponents 3 and -4.

$$7^{1}\times 2^{1}\times \frac{1}{a}b^{3+1}$$

Add the exponents 3 and 1.

$$7^{1}\times 2^{1}\times \frac{1}{a}b^{4}$$

Multiply 7 times 2.

$$14\times \frac{1}{a}b^{4}$$

Differentiate w.r.t. a

$$-\frac{14b^{4}}{a^{2}}$$