Solve 4a^2b^4(3a^-16b^-2)=

$$4 a ^ { 2 } b ^ { 4 } ( 3 a ^ { - 16 } b ^ { - 2 } ) =$$

Evaluate

$$\frac{12b^{2}}{a^{14}}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

$$4^{1}a^{2}b^{4}\times 3^{1}a^{-16}b^{-2}$$

Use the Commutative Property of Multiplication.

$$4^{1}\times 3^{1}a^{2}a^{-16}b^{4}b^{-2}$$

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

$$4^{1}\times 3^{1}a^{2-16}b^{4-2}$$

Add the exponents 2 and -16.

$$4^{1}\times 3^{1}a^{-14}b^{4-2}$$

Add the exponents 4 and -2.

$$4^{1}\times 3^{1}\times \frac{1}{a^{14}}b^{2}$$

Multiply 4 times 3.

$$12\times \frac{1}{a^{14}}b^{2}$$

Differentiate w.r.t. b

$$\frac{24b}{a^{14}}$$