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Which of the following is equal to 2^k*5^(k-1)?

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by Vincen » Tue Nov 28, 2017 8:16 am
Which of the following is equal to 2^k*5^(k-1)?

A. 2*10^(k-1)
B. 5*10^(k-1)
C. 10^k
D. 2*10^k )
E. 10^(2k-1)

The OA is A.

How can I rewrite the given expression to get A? I need your help experts. Please. Thanks in advance.
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by EconomistGMATTutor » Tue Nov 28, 2017 8:51 am
Hello Vincen.

Let's rewrite the expression as follows $$2^k\cdot5^{k-1}=2\cdot2^{k-1}\cdot5^{k-1}=2\cdot\left(2\cdot5\right)^{k-1}=2\cdot10^{k-1}.$$ This tell us that the correct answer is A.

I hope this can help you to clarify your doubt.

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

Regards.
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by Scott@TargetTestPrep » Sat Oct 05, 2019 3:40 pm
Vincen wrote:Which of the following is equal to 2^k*5^(k-1)?

A. 2*10^(k-1)
B. 5*10^(k-1)
C. 10^k
D. 2*10^k )
E. 10^(2k-1)

The OA is A.

How can I rewrite the given expression to get A? I need your help experts. Please. Thanks in advance.
Let's simplify the given expression:

2^k * 5^(k-1) = 2^1 * 2^(k-1) * 5^(k-1) = 2 * (2*5)^(k-1) = 2 * 10^(k-1)

Answer: A

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