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2^x-1/2^1-x is equal to which of the following?

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2^x-1/2^1-x is equal to which of the following?  [#permalink]

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New post Updated on: 04 Apr 2017, 20:58
00:00
A
B
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D
E

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\(\frac{2^{x-1}}{2^{1-x}}\) is equal to which of the following?

A. \(4^{x-1}\)
B. \(4^{1-x}\)
C. \(4^{2x}\)
D. \(4^{-2x}\)
E. \(4^x\)

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Originally posted by MathRevolution on 04 Apr 2017, 17:14.
Last edited by Bunuel on 04 Apr 2017, 20:58, edited 1 time in total.
Edited the question.
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Re: 2^x-1/2^1-x is equal to which of the following?  [#permalink]

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New post 04 Apr 2017, 18:03
MathRevolution wrote:
\(2^{x-1}/2^{1-x}\) is equal to which of the following?

A. \(4^{x-1}\)
B. \(4^{1-x}\)
C. \(4^{2x}\)
D. \(4^{-2x}\)
E. \(4^x\)


\(2^{x-1}/2^{1-x} = 2^{((x-1)-(1-x))} = 2^{(2x-2)} >> 4^{(x-1)}\)
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Re: 2^x-1/2^1-x is equal to which of the following?  [#permalink]

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New post 04 Apr 2017, 18:05
MathRevolution wrote:
\(2^{x-1}/2^{1-x}\) is equal to which of the following?

A. \(4^{x-1}\)
B. \(4^{1-x}\)
C. \(4^{2x}\)
D. \(4^{-2x}\)
E. \(4^x\)



Main point to know here
\(\frac{1}{2^x}=2^{-x}\)

\(\frac{2^{x-1}}{2^{1-x}}=2^{x-1}*2^{-(1-x)} = 2^{x-1}*2^{x-1}=2^{2(x-1)}=4^{x-1}\)

A
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Re: 2^x-1/2^1-x is equal to which of the following?  [#permalink]

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New post 06 Apr 2017, 00:02
==> You get \(\frac{2^{x-1}}{2^{1-x}} =2^{x-1-(1-x)}=2^{2(x-1)}=4^{x-1}\).

The answer is A.
Answer: A
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Re: 2^x-1/2^1-x is equal to which of the following? &nbs [#permalink] 06 Apr 2017, 00:02
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2^x-1/2^1-x is equal to which of the following?

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