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# If xy = 1, what is the value of 2^(x + y)^2/2^(x-y)^2?

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Manager
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If xy = 1, what is the value of 2^(x + y)^2/2^(x-y)^2?  [#permalink]

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18 Jun 2011, 07:03
5
26
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Difficulty:

25% (medium)

Question Stats:

73% (00:40) correct 27% (00:52) wrong based on 746 sessions

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If xy = 1, what is the value of $$\frac {2^{(x + y)^2}} {2^{(x - y)^2}$$ ?

A. 2
B. 4
C. 8
D. 16
E. 32

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-xy-1-what-is-the-value-of-2-x-y-2-2-x-y-107238.html
Current Student
Joined: 26 May 2005
Posts: 528
Re: if xy=1, what is the value of (2^(x+y)^2)/(2^(x+y)^2)?  [#permalink]

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18 Jun 2011, 07:24
1
WishMasterUA wrote:
if xy=1, what is the value of (2^((x+y)^2))/(2^((x-y)^2))?
1) 2
2) 4
3) 8
4) 16
5) 32

its D

2^(x+y)^2/2^(x-y)^2

2^(x+y)^2-(x-y)^2
2^4xy
2^4*1 = 2^4 = 16
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Joined: 20 Dec 2010
Posts: 1879
Re: if xy=1, what is the value of (2^(x+y)^2)/(2^(x+y)^2)?  [#permalink]

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18 Jun 2011, 07:44
39
8
WishMasterUA wrote:
if xy=1, what is the value of (2^((x+y)^2))/(2^((x-y)^2))?
1) 2
2) 4
3) 8
4) 16
5) 32

$$\frac{2^{(x+y)^2}}{2^{(x+y)^2}}$$

$$=\frac{2^{(x^2+y^2+2xy)}}{2^{(x^2+y^2-2xy)}}$$ [:Note: $$(x+y)^2=x^2+y^2+2xy \hspace{3} & \hspace{3} (x-y)^2=x^2+y^2-2xy$$]

$$=2^{(x^2+y^2+2xy-(x^2+y^2-2xy))}$$ [:Note: $$\frac{x^m}{x^n}= x^{(m-n)}$$ ]

$$=2^{(x^2+y^2+2xy-x^2-y^2+2xy)}$$

$$=2^{(4xy)}$$

$$=2^{(4xy)}=2^4=16$$ [:Note: xy=1]

Ans: "D"
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Manager
Status: GMAT BATTLE - WIN OR DIE
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Posts: 130
Concentration: General Management, Entrepreneurship
GMAT Date: 12-22-2011
GPA: 3.81
WE: General Management (Hospitality and Tourism)
Re: if xy=1, what is the value of (2^(x+y)^2)/(2^(x+y)^2)?  [#permalink]

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18 Jun 2011, 07:51
4
fluke wrote:
WishMasterUA wrote:
if xy=1, what is the value of (2^((x+y)^2))/(2^((x-y)^2))?
1) 2
2) 4
3) 8
4) 16
5) 32

$$\frac{2^{(x+y)^2}}{2^{(x+y)^2}}$$

$$=\frac{2^{(x^2+y^2+2xy)}}{2^{(x^2+y^2-2xy)}}$$ [:Note: $$(x+y)^2=x^2+y^2+2xy \hspace{3} & \hspace{3} (x-y)^2=x^2+y^2-2xy$$]

$$=2^{(x^2+y^2+2xy-(x^2+y^2-2xy))}$$ [:Note: $$\frac{x^m}{x^n}= x^{(m-n)}$$ ]

$$=2^{(x^2+y^2+2xy-x^2-y^2+2xy)}$$

$$=2^{(4xy)}$$

$$=2^{(4xy)}=2^4=16$$ [:Note: xy=1]

Ans: "D"

fantastic detail thank a lot
Math Expert
Joined: 02 Sep 2009
Posts: 47920
Re: If xy = 1, what is the value of 2^(x + y)^2/2^(x-y)^2?  [#permalink]

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23 Jan 2014, 08:42
3
1
If xy = 1, what is the value of $$\frac {2^{(x + y)^2}} {2^{(x - y)^2}$$ ?

A. 2
B. 4
C. 8
D. 16
E. 32

$$\frac{2^{(x+y)^2}}{2^{(x-y)^2}}=2^{(x+y)^2-(x-y)^2}=2^{(x+y+x-y)(x+y-x+y)}=2^{(2x)(2y)}=2^{4xy}=2^4=16$$.

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-xy-1-what-is-the-value-of-2-x-y-2-2-x-y-107238.html
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Re: If xy = 1, what is the value of 2^(x + y)^2/2^(x-y)^2?  [#permalink]

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26 Jul 2018, 04:40
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Re: If xy = 1, what is the value of 2^(x + y)^2/2^(x-y)^2? &nbs [#permalink] 26 Jul 2018, 04:40
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