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If x is a positive integer, what is (2^x/2^(–x))^x ? 10 May 2017, 12:06
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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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B
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If x is a positive integer, what is (2^x/2^(–x))^x ? 18 May 2017, 11:53
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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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If x is a positive integer, what is (2^x/2^(–x))^x ? 10 May 2017, 12:26
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\((\frac{2^x}{2^{(–x)}})^x\)

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

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

= \(2^{2x^2}\) (Option B)
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If x is a positive integer, what is (2^x/2^(–x))^x ? 10 May 2017, 12:46
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Bunuel
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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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 ? 24 May 2017, 18:22
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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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If x is a positive integer, what is (2^x/2^(–x))^x ? 25 Nov 2018, 09:38
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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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If x is a positive integer, what is (2^x/2^(–x))^x ? 22 Apr 2023, 22:35
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An easy way to solve this question is by plugging in a positive integer for x.

Plugging in 3 for x gives 2^18. Only option B produces the same result.
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If x is a positive integer, what is (2^x/2^(–x))^x ? 19 May 2025, 23:26
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