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If 2^{(x+y)^2} / 2^{(xy)^2} = 2, what is the value of xy?
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Updated on: 20 Dec 2015, 20:59
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If \(\frac{2^{(x+y)^2}}{2^{(xy)^2}} = 2\), what is the value of xy? (A) 1/4 (B) 1/2 (C) 0 (D) 1/4 (E) 1/2
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Originally posted by NoHalfMeasures on 20 Dec 2015, 20:25.
Last edited by Bunuel on 20 Dec 2015, 20:59, edited 1 time in total.
Edited the question.



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Re: If 2^{(x+y)^2} / 2^{(xy)^2} = 2, what is the value of xy?
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20 Dec 2015, 20:27
2^{(x+y)^2} / 2^{(xy)^2} = 2 =>(x+y)^2  (xy)^2 = 1 => 4xy = 1 xy=1/4 Ans D
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Re: If 2^{(x+y)^2} / 2^{(xy)^2} = 2, what is the value of xy?
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25 Dec 2015, 16:19
Would someone please break down the steps to solve this question, step by step?



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Re: If 2^{(x+y)^2} / 2^{(xy)^2} = 2, what is the value of xy?
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27 Dec 2015, 20:43
Anonamy wrote: Would someone please break down the steps to solve this question, step by step? Hi, the Q is If \(\frac{2^{(x+y)^2}}{2^{(xy)^2}} = 2\), what is the value of xy? (A) 1/4 (B) 1/2 (C) 0 (D) 1/4 (E) 1/2.. \(\frac{2^{(x+y)^2}}{2^{(xy)^2}} = 2\) the power can be added if multiplied and can be subtracted if divided.. when you take a power to numerator from denominator, you have to just add  sign.. example 1/2^2=2^(2).. so \(\frac{2^{(x+y)^2}}{2^{(xy)^2}} = 2\) will become.. \(2^{(x+y)^2(xy)^2} = 2\).. \(2^{(x^2+y^2+2xyx^2y^2+2xy)}=2\).. so\(2^(4xy)=2^1\). 4xy=1 or xy=1/4.. D Hope it is clear now..
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Re: If 2^{(x+y)^2} / 2^{(xy)^2} = 2, what is the value of xy?
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30 Jan 2017, 09:04
NoHalfMeasures wrote: If \(\frac{2^{(x+y)^2}}{2^{(xy)^2}} = 2\), what is the value of xy?
(A) 1/4 (B) 1/2 (C) 0 (D) 1/4 (E) 1/2 \(2^{(x^2 +y^2 + 2xy)  (x^2 +y^2  2xy)}= 2^1\) Or, \(2^{x^2 +y^2 + 2xy  x^2  y^2 + 2xy}= 2^1\) Or, \(2^{4xy}= 2^1\) Or, \(4xy = 1\) So, \(xy = \frac{1}{4}\) Thus, answer will be (D) \(\frac{1}{4}\) ...
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Re: If 2^{(x+y)^2} / 2^{(xy)^2} = 2, what is the value of xy?
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31 Jan 2017, 16:10
On solving 2^4xy = 2^1 4xy = 1 xy = 1/4 D
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Re: If 2^{(x+y)^2} / 2^{(xy)^2} = 2, what is the value of xy?
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08 Feb 2017, 20:41
Have a query: If base & exponent are the same, then the exponents have to be added? Because I came across this rule, a^n.b^n=(ab)^n and applying this in the subjected problem, gave the wrong answer.



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Re: If 2^{(x+y)^2} / 2^{(xy)^2} = 2, what is the value of xy?
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24 Dec 2018, 11:28
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Re: If 2^{(x+y)^2} / 2^{(xy)^2} = 2, what is the value of xy?
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