Solve (9a^12b^-4)(1/3a^-4b^6)

$$( 9 a ^ { 12 } b ^ { - 4 } ) ( \frac { 1 } { 3 } a ^ { - 4 } b ^ { 6 } )$$

Evaluate

$$3b^{2}a^{8}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

$$9^{1}a^{12}b^{-4}\times \left(\frac{1}{3}\right)^{1}a^{-4}b^{6}$$

Use the Commutative Property of Multiplication.

$$9^{1}\times \left(\frac{1}{3}\right)^{1}a^{12}a^{-4}b^{-4}b^{6}$$

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

$$9^{1}\times \left(\frac{1}{3}\right)^{1}a^{12-4}b^{-4+6}$$

Add the exponents 12 and -4.

$$9^{1}\times \left(\frac{1}{3}\right)^{1}a^{8}b^{-4+6}$$

Add the exponents -4 and 6.

$$9^{1}\times \left(\frac{1}{3}\right)^{1}a^{8}b^{2}$$

Multiply 9 times \frac{1}{3}.

$$3a^{8}b^{2}$$

Differentiate w.r.t. a

$$24b^{2}a^{7}$$