Solve (3a^5b)(4a^4b^7)

$$( 3 a ^ { 5 } b ) ( 4 a ^ { 4 } b ^ { 7 } )$$

Evaluate

$$12b^{8}a^{9}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

$$3^{1}a^{5}b^{1}\times 4^{1}a^{4}b^{7}$$

Use the Commutative Property of Multiplication.

$$3^{1}\times 4^{1}a^{5}a^{4}b^{1}b^{7}$$

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

$$3^{1}\times 4^{1}a^{5+4}b^{1+7}$$

Add the exponents 5 and 4.

$$3^{1}\times 4^{1}a^{9}b^{1+7}$$

Add the exponents 1 and 7.

$$3^{1}\times 4^{1}a^{9}b^{8}$$

Multiply 3 times 4.

$$12a^{9}b^{8}$$

Differentiate w.r.t. a

$$108\left(ab\right)^{8}$$