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GRE 1: Q167 V156
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Which of the following is equal to..for all integers x and y
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Updated on: 08 Feb 2019, 11:25
Updated on: 08 Feb 2019, 11:25
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Which of the following is equal to \(\frac{2^{x-y}}{2^{x+y}}\) for all integers \(x\) and \(y\) ?
A. \(4^{-x}\)
B. \(4^{-y}\)
C. \(2^{xy}\)
D. \(4^x\)
E. \(4^y\)
_________________
A. \(4^{-x}\)
B. \(4^{-y}\)
C. \(2^{xy}\)
D. \(4^x\)
E. \(4^y\)
Practice Questions
Question: 10
Page: 83
Question: 10
Page: 83
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Sandy
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Retired Moderator
Joined: 07 Jun 2014
Posts: 4805
GRE 1: Q167 V156
WE:Business Development (Energy and Utilities)
Re: Which of the following is equal to..for all integers x and y
[#permalink]
20 May 2016, 18:00
20 May 2016, 18:00
1
Expert Reply
Explanation
Simplifying the fraction \(\frac{2^x^-^y}{2^x^+^y}\), yields \(\frac{2^x^-^y}{2^x^+^y}\)=\(2^-^2^y\). The only answer choice with 2 as the base is Choice C, \(2^x^y\), , which is clearly not the correct answer. Since all the other answer choices have 4 as the base, it is a good idea to rewrite 2–2y as an expression with 4 as the base, as follows.
\(2^-^2^y= \frac{1}{2^2^y}= 4^-^y\).
Thus the correct answer is Choice B.
_________________
Simplifying the fraction \(\frac{2^x^-^y}{2^x^+^y}\), yields \(\frac{2^x^-^y}{2^x^+^y}\)=\(2^-^2^y\). The only answer choice with 2 as the base is Choice C, \(2^x^y\), , which is clearly not the correct answer. Since all the other answer choices have 4 as the base, it is a good idea to rewrite 2–2y as an expression with 4 as the base, as follows.
\(2^-^2^y= \frac{1}{2^2^y}= 4^-^y\).
Thus the correct answer is Choice B.
_________________
Sandy
If you found this post useful, please let me know by pressing the Kudos Button
Try our free Online GRE Test
If you found this post useful, please let me know by pressing the Kudos Button
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Which of the following is equal to..for all integers x and y
[#permalink]
01 Jun 2016, 14:55
01 Jun 2016, 14:55
1
Expert Reply
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Bookmarks
sandy wrote:
Which of the following is equal to \(\frac{2^{x-y}}{2^{x+y}}\) for all integers x and y ?
A. \(4^{-x}\)
B. \(4^{-y}\)
C. \(2^{xy}\)
D. \(4^x\)
E. \(4^y\)
A. \(4^{-x}\)
B. \(4^{-y}\)
C. \(2^{xy}\)
D. \(4^x\)
E. \(4^y\)
APPROACH #1: Algebra
Given: \(\frac{2^{x-y}}{2^{x+y}}\)
Apply the Quotient Law to get: \(2^{(x-y) - (x+y)}\)
Simplify: \(2^{-2y}\)
We can rewrite this expression using the Power of a Power Law as follows: \((2^2)^{-y}\)
Evaluate to get: : \(4^{-y}\)
Answer: B
APPROACH #2: INPUT-OUTPUT method
Let \(x = 2\) and \(y = 1\)
In this case, \(\frac{2^{x-y}}{2^{x+y}}=\frac{2^{2-1}}{2^{2+1}}=\frac{2^{1}}{2^{3}}=\frac{2}{8}=\frac{1}{4}\)
So, when the INPUT is \(x = 2\) and \(y = 1\), the OUTPUT is \(\frac{1}{4}\)
The correct answer choice will be the one that has an OUTPUT of \(\frac{1}{4}\) when the INPUT is \(x = 2\) and \(y = 1\)
A. \(4^{-x}=4^{-2} = \frac{1}{16}\). ELIMINATE A.
B. \(4^{-y}=4^{-1}=\frac{1}{4}\). KEEP B.
C. \(2^{xy}=2^{(2)(1)}=2^{2}=4\). ELIMINATE C.
D. \(4^x=4^2=16\). ELIMINATE D.
E. \(4^y=4^1=4\). ELIMINATE E.
Answer: B
RELATED VIDEO
_________________
Re: Which of the following is equal to..for all integers x and y
[#permalink]
02 Aug 2018, 19:38
02 Aug 2018, 19:38
sandy wrote:
Explanation
Simplifying the fraction \(\frac{2^x^-^y}{2^x^+^y}\), yields \(\frac{2^x^-^y}{2^x^+^y}\)=\(2^-^2^y\). The only answer choice with 2 as the base is Choice C, \(2^x^y\), , which is clearly not the correct answer. Since all the other answer choices have 4 as the base, it is a good idea to rewrite 2–2y as an expression with 4 as the base, as follows.
\(2^-^2^y= \frac{1}{2^2^y}= 4^-^y\).
Thus the correct answer is Choice B.
Simplifying the fraction \(\frac{2^x^-^y}{2^x^+^y}\), yields \(\frac{2^x^-^y}{2^x^+^y}\)=\(2^-^2^y\). The only answer choice with 2 as the base is Choice C, \(2^x^y\), , which is clearly not the correct answer. Since all the other answer choices have 4 as the base, it is a good idea to rewrite 2–2y as an expression with 4 as the base, as follows.
\(2^-^2^y= \frac{1}{2^2^y}= 4^-^y\).
Thus the correct answer is Choice B.
Can you please explain how you simplify that fraction?
Re: Which of the following is equal to..for all integers x and y
[#permalink]
26 Dec 2018, 05:56
26 Dec 2018, 05:56
1
msawicka wrote:
sandy wrote:
Explanation
Simplifying the fraction \(\frac{2^x^-^y}{2^x^+^y}\), yields \(\frac{2^x^-^y}{2^x^+^y}\)=\(2^-^2^y\). The only answer choice with 2 as the base is Choice C, \(2^x^y\), , which is clearly not the correct answer. Since all the other answer choices have 4 as the base, it is a good idea to rewrite 2–2y as an expression with 4 as the base, as follows.
\(2^-^2^y= \frac{1}{2^2^y}= 4^-^y\).
Thus the correct answer is Choice B.
Simplifying the fraction \(\frac{2^x^-^y}{2^x^+^y}\), yields \(\frac{2^x^-^y}{2^x^+^y}\)=\(2^-^2^y\). The only answer choice with 2 as the base is Choice C, \(2^x^y\), , which is clearly not the correct answer. Since all the other answer choices have 4 as the base, it is a good idea to rewrite 2–2y as an expression with 4 as the base, as follows.
\(2^-^2^y= \frac{1}{2^2^y}= 4^-^y\).
Thus the correct answer is Choice B.
Can you please explain how you simplify that fraction?
=\(\frac{2^x^-^y}{2^x^+^y}\)
=\(2^x^-^y^-^x^-^y\)
=\(2^-^2^y\)
now
\(2^-^2^y= \frac{1}{2^2^y}= 4^-^y\).
Re: Which of the following is equal to..for all integers x and y
[#permalink]
07 May 2019, 10:46
07 May 2019, 10:46
AE wrote:
msawicka wrote:
sandy wrote:
Explanation
Simplifying the fraction \(\frac{2^x^-^y}{2^x^+^y}\), yields \(\frac{2^x^-^y}{2^x^+^y}\)=\(2^-^2^y\). The only answer choice with 2 as the base is Choice C, \(2^x^y\), , which is clearly not the correct answer. Since all the other answer choices have 4 as the base, it is a good idea to rewrite 2–2y as an expression with 4 as the base, as follows.
\(2^-^2^y= \frac{1}{2^2^y}= 4^-^y\).
Thus the correct answer is Choice B.
Simplifying the fraction \(\frac{2^x^-^y}{2^x^+^y}\), yields \(\frac{2^x^-^y}{2^x^+^y}\)=\(2^-^2^y\). The only answer choice with 2 as the base is Choice C, \(2^x^y\), , which is clearly not the correct answer. Since all the other answer choices have 4 as the base, it is a good idea to rewrite 2–2y as an expression with 4 as the base, as follows.
\(2^-^2^y= \frac{1}{2^2^y}= 4^-^y\).
Thus the correct answer is Choice B.
Can you please explain how you simplify that fraction?
=\(\frac{2^x^-^y}{2^x^+^y}\)
=\(2^x^-^y^-^x^-^y\)
=\(2^-^2^y\)
now
\(2^-^2^y= \frac{1}{2^2^y}= 4^-^y\).
What happens to the 2 on the bottom? I feel like I'm missing the step that allows us to put the exponents all on one line.
Re: Which of the following is equal to..for all integers x and y
[#permalink]
07 May 2019, 11:19
07 May 2019, 11:19
Expert Reply
It is a property of fraction and exponents.
The same base then you do have the two raised to the two exponents subtracted
Here for more information about
GMAT Club Math Book v3 - Jan-2-2013.pdf [2.83 MiB]
Downloaded 76 times
The same base then you do have the two raised to the two exponents subtracted
Here for more information about
Attachment:
GMAT Club Math Book v3 - Jan-2-2013.pdf [2.83 MiB]
Downloaded 76 times
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Re: Which of the following is equal to..for all integers x and y
[#permalink]
24 Apr 2021, 08:05
24 Apr 2021, 08:05
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