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What is the decimal equivalent of (1/5)^5?

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by Brent@GMATPrepNow » Tue Aug 21, 2018 3:58 pm
BTGmoderatorLU wrote:Source: Official Guide

$$\text{What is the decimal equivalent of } \left(\frac{1}{5}\right)^5?$$

A. 0.00032
B. 0.0016
C. 0.00625
D. 0.008
E. 0.03125

The OA is A.
Here's one approach:
(1/5)� = (2/10)�
= (2�)/(10�)
= 32/100,000
= 0.00032
= A

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by Brent@GMATPrepNow » Tue Aug 21, 2018 4:02 pm
BTGmoderatorLU wrote:Source: Official Guide

$$\text{What is the decimal equivalent of } \left(\frac{1}{5}\right)^5?$$

A. 0.00032
B. 0.0016
C. 0.00625
D. 0.008
E. 0.03125

The OA is A.
Another approach:

Given: (1/5)^5
Rewrite as: 1/(5^5)
Create equivalent fraction by multiplying top and bottom by 2^5 to get: 2^5/(2^5)(5^5)
Simplify: 32/10^5
Simplify: 32/100,000

STOP.
So, the decimal equivalent will have 32 in.
Check the answer choices.....only A works.

Answer: A

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by fskilnik@GMATH » Wed Aug 22, 2018 12:11 pm
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by GMATGuruNY » Wed Aug 22, 2018 1:11 pm
BTGmoderatorLU wrote:Source: Official Guide

$$\text{What is the decimal equivalent of } \left(\frac{1}{5}\right)^5?$$

A. 0.00032
B. 0.0016
C. 0.00625
D. 0.008
E. 0.03125
1/5� =

= (1/25)(1/25)(1/5)
= (4/4 * 1/25)(4/4 * 1/25)(2/2 * 1/5)
= (4/100)(4/100)(2/10)
= 32/100000
= 32 * 10ˉ�
= 0.00032

The correct answer is A.
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by Scott@TargetTestPrep » Thu Aug 23, 2018 4:08 pm
BTGmoderatorLU wrote:Source: Official Guide

$$\text{What is the decimal equivalent of } \left(\frac{1}{5}\right)^5?$$

A. 0.00032
B. 0.0016
C. 0.00625
D. 0.008
E. 0.03125
We can multiply (1/5)^5 by 2^5/2^5 and we have:

2^5/10^5 = 32/10^5 = 0.00032

Alternate Solution:

The decimal equivalent of 1/5 is 0.2, or 2 x 10^-1. We know that 2^5 = 32, so we look for "32" in the answer choices. Only choice A meets the requirement.

Answer: A

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