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If x is a positive integer, what is (2^x/2^(–x))^x ?

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If x is a positive integer, what is (2^x/2^(–x))^x ?  [#permalink]

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New post 10 May 2017, 11:06
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

71% (00:47) correct 29% (00:50) wrong based on 125 sessions

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Re: If x is a positive integer, what is (2^x/2^(–x))^x ?  [#permalink]

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New post 10 May 2017, 11:26
\((\frac{2^x}{2^{(–x)}})^x\)

= \({2^{x-(-x)}}^x\)

= \({2^{2x^x}\)

= \(2^{2x^2}\) (Option B)
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Re: If x is a positive integer, what is (2^x/2^(–x))^x ?  [#permalink]

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New post 10 May 2017, 11:46
Bunuel wrote:
If x is a positive integer, what is \((\frac{2^x}{2^{(–x)}})^x\) ?

A. 1

B. \(2^{2x^2}\)

C. \(2^{(2x)^2}\)

D. \(4^{2x}\)

E. \(4^{(2x)^2}\)



Put x=2
You will get answer as option B
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If x is a positive integer, what is (2^x/2^(–x))^x ?  [#permalink]

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New post 18 May 2017, 10:53
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If x is a positive integer, what is \((\frac{2^x}{2^{(–x)}})^x\) ?

\((\frac{2^x}{2^{(–x)}})^x\)
= \((2^x * 2^x )^x\)
= \((2^{2x})^x\) = \(2^{2x^2}\)
[As per rules of Exponents => \(a^m * a^n = a^{(m+n)}\)]
[As per rules of Exponents =>\((a^m)^n = a^{mn}\)]
Answer B...

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Re: If x is a positive integer, what is (2^x/2^(–x))^x ?  [#permalink]

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New post 24 May 2017, 17:22
I had originally got E) 4^(2x)^2 by working outside of the brackets first but realized that this question has the 2^x and 2^-x in brackets, so must be solved within the brackets first as per BEDMAS rules. I hope this helps in case anyone else also chose E.

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Re: If x is a positive integer, what is (2^x/2^(–x))^x ?  [#permalink]

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New post 25 Nov 2018, 08:38
Like many I started by moving the 2^(-x) to the numerator. Which makes the equation (2^x * 2^x)^x. Using exponent rules you add the exponents when you multiply leaving (2^2x)^x. Then using exponent rules you multiply exponents that are to the power of another exponent. Thus 2^(2xx) or simply 2^2x^2. You cannot have the extra bracket as shown in option C because that implies that the 2 is also squared which isn’t the case.

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Re: If x is a positive integer, what is (2^x/2^(–x))^x ? &nbs [#permalink] 25 Nov 2018, 08:38
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