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Which of the following has the same value as 5^6?

This topic has 3 expert replies and 0 member replies

Which of the following has the same value as 5^6?

Post Mon Feb 26, 2018 2:10 am
Which of the following has the same value as 5^6?

A. 30
B. 25^2
C. 50^3
D. 125^2
E. 250^3

The OA is the option D.

Experts, how can I rewrite 5^6 to find the correct answer? Can you help me? I don't know how to solve it.

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Post Mon Feb 26, 2018 2:58 am
M7MBA wrote:
Which of the following has the same value as 5^6?

A. 30
B. 25^2
C. 50^3
D. 125^2
E. 250^3

The OA is the option D.

Experts, how can I rewrite 5^6 to find the correct answer? Can you help me? I don't know how to solve it.
Hello M7MBA.

Let's see.

How you asked, we have to rewrite the expression as follows: $$5^6=5^{3\cdot2}=\left(\left(5\right)^3\right)^2=125^2.$$

Therefore, the correct answer is the option D.

I hope this answer can help you.

I'm available if you'd like a follow-up.

Regards.

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GMAT/MBA Expert

Post Mon Feb 26, 2018 2:55 am
M7MBA wrote:
Which of the following has the same value as 5^6?

A. 30
B. 25^2
C. 50^3
D. 125^2
E. 250^3
Since the 5⁶ = 5*5*5*5*5*5 = odd, the correct answer must also be odd and thus cannot have a units digit of 0.
Eliminate A (30), B(50) and E(250).

B: 25² = (5²)² = 5⁴.
Eliminate B.

The correct answer is D.

D: 125² = (5³)² = 5⁶.

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Post Tue Feb 27, 2018 10:55 am
M7MBA wrote:
Which of the following has the same value as 5^6?

A. 30
B. 25^2
C. 50^3
D. 125^2
E. 250^3
Scanning our answer choices, we see that 25 and 125 both contain only prime factors of 5, so let’s break those down:

25^2 = (5^2)^2 = 5^4

125^2 = (5^3)^2 = 5^6

Answer: D

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