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What is the decimal equivalent of (2/5)^4?

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What is the decimal equivalent of (2/5)^4?  [#permalink]

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New post 12 Oct 2017, 23:22
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A
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D
E

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Re: What is the decimal equivalent of (2/5)^4?  [#permalink]

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New post 12 Oct 2017, 23:35
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Bunuel wrote:
What is the decimal equivalent of (2/5)^4?

(A) 0.44
(B) 0.16
(C) 0.048
(D) 0.0256
(E) 0.0064



2/5 is 0.4
4^4 = 256
(0.4)^4 will be equal to 0.0256 (4 decimal places)
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Re: What is the decimal equivalent of (2/5)^4?  [#permalink]

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New post 20 Jul 2018, 21:04
niks18 Bunuel chetan2u pikolo2510

Any alternative approach than not knowing powers of 4?
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What is the decimal equivalent of (2/5)^4?  [#permalink]

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New post 20 Jul 2018, 21:25
\((\frac{2}{5})^4\) = \((\frac{4}{10})^4\) = \(\frac{256}{10000} = 0.0256\)

Hence option D
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Re: What is the decimal equivalent of (2/5)^4?  [#permalink]

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New post 20 Jul 2018, 21:34
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adkikani wrote:
niks18 Bunuel chetan2u pikolo2510

Any alternative approach than not knowing powers of 4?


Hi since you want to avoid calculating 4^4..
2/5 can be written as 2*2/5*2=4/10...
Now what should be the units digit....
4^1=4...4^2=16 so 6, 4^3=4*6, so 4 ..
Therefore 4,6,4,6,4,6...
Therefore 4^4 will have 6 as units digit...
What about the number of decimal ....10^4=1000 so 4 decimals.
Something like 0.xyz6

Only one choice is of this format
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3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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What is the decimal equivalent of (2/5)^4?  [#permalink]

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New post 20 Jul 2018, 22:14
(2/5 )=0.4=4/10

Therefore (4/10)^4=(4^4)/(10^4)
=256/10000. =0.0256



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What is the decimal equivalent of (2/5)^4? &nbs [#permalink] 20 Jul 2018, 22:14
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