Question

Choose the correct expression using the fewest number of bases possible that is equivalent to the current expression.

Let a and b be positive integers. 2^3a × 2^3b = ?

a. 2^3a+b
b. 2^3a-b
c. 2^3ab
d. 2^3b-a

Answer 1

The expression 2^3a × 2^3b simplifies to 2^3(a+b) by adding the exponents, making option A the correct choice.

Step-by-step explanation:

To find the correct expression for 2^3a × 2^3b, we use the properties of exponents. When multiplying numbers with the same base, we simply add the exponents. Thus, we add 3a and 3b to get 3(a+b). Hence, 2^3a × 2^3b simplifies to 2^(3a+3b), which is equivalent to 2^3(a+b). Therefore, the correct answer is Option A: 2^3(a+b).