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

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 4865
GPA: 3.82
2^x-1/2^1-x is equal to which of the following? [#permalink]

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04 Apr 2017, 17:14
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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. $$4^x$$
[Reveal] Spoiler: OA

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Last edited by Bunuel on 04 Apr 2017, 20:58, edited 1 time in total.
Edited the question.
Intern
Joined: 29 Apr 2015
Posts: 23
GPA: 3.89
Re: 2^x-1/2^1-x is equal to which of the following? [#permalink]

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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. $$4^x$$

$$2^{x-1}/2^{1-x} = 2^{((x-1)-(1-x))} = 2^{(2x-2)} >> 4^{(x-1)}$$
Math Expert
Joined: 02 Aug 2009
Posts: 5649
Re: 2^x-1/2^1-x is equal to which of the following? [#permalink]

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

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

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Re: 2^x-1/2^1-x is equal to which of the following?   [#permalink] 06 Apr 2017, 00:02
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