Question: If a and b are positive integers and (2a)^b= 2^3, what is the value of 2^a∗2^b?

A) 6
B) 8
C) 16
D) 32
E) 64

“If a and b are positive integers and (2a)^b= 2^3, what is the value”- is a topic of the GMAT Quantitative reasoning section of GMAT. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

Solution and Explanation:
Approach Solution 1:
(2^a)^b= 2^3
2^ab= 2^3
ab=3

ab must be (1)(3) or (3)(1)

2^a*2^b= 2^a+b
2^1+3= 2^4= 16

Correct Answer: C

Approach Solution 2:
(2^a)^b = 2^3
=>2^ab = 2^3
ab = 3
If a = 1 then b = 3 or if a=3 then b=1

2^a*2^b = 2^(a+b)
= 2^4 = 16

Correct Answer: C

Approach Solution 3:
Given:
(2^a)^b= 2^3

Apply the Power of a Power rule to get:

2^ab= 2^3

From this we can conclude that: ab=3

Since a and b are positive integers, we can be certain that one of the values (a or b) is 1, and the other value is 3
This means the SUM of a and b is 4 (1 + 3 = 4)
We want to find the value of 2^a∗2^b

Apply the Product rule to get: 2^a+b
Since we now know the SUM of a and b is 4, we can write:
2^a+b= 2^4= 16

Correct Answer: C

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