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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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10 May 2017, 11:06
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15% (low)

Question Stats:

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

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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. $$4^{(2x)^2}$$

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

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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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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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18 May 2017, 10:53
1
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 =>$$(a^m)^n = a^{mn}$$]

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

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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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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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