Solve (3m^5b^-3)(4m^-3b^7

$$( 3 m ^ { 5 } b ^ { - 3 } ) ( 4 m ^ { - 3 } b ^ { 7 }$$

Evaluate

$$12m^{2}b^{4}$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

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

Use the Commutative Property of Multiplication.

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

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

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

Add the exponents 5 and -3.

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

Add the exponents -3 and 7.

$$3^{1}\times 4^{1}m^{2}b^{4}$$

Multiply 3 times 4.

$$12m^{2}b^{4}$$

Differentiate w.r.t. m

$$24mb^{4}$$