Solve (2a^-30b^-29)(3a^31b^30)

$$( 2 a ^ { - 30 } b ^ { - 29 } ) ( 3 a ^ { 31 } b ^ { 30 } )$$

Evaluate

$$6ab$$

Steps Using Commutative Property of Multiplication

Use the rules of exponents to simplify the expression.

$$2^{1}a^{-30}b^{-29}\times 3^{1}a^{31}b^{30}$$

Use the Commutative Property of Multiplication.

$$2^{1}\times 3^{1}a^{-30}a^{31}b^{-29}b^{30}$$

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

$$2^{1}\times 3^{1}a^{-30+31}b^{-29+30}$$

Add the exponents -30 and 31.

$$2^{1}\times 3^{1}a^{1}b^{-29+30}$$

Add the exponents -29 and 30.

$$2^{1}\times 3^{1}ab^{1}$$

Multiply 2 times 3.

$$6ab$$

Differentiate w.r.t. b

$$6a$$