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Re: Which of the following is equal to..for all integers x and y
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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.
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Which of the following is equal to..for all integers x and y
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01 Jun 2016, 14:55
1
Expert Reply
1
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. \(4^y\)
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 \(y = 1\)
Re: Which of the following is equal to..for all integers x and y
[#permalink]
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.
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
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.
Can you please explain how you simplify that fraction?
Re: Which of the following is equal to..for all integers x and y
[#permalink]
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.
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
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24 Apr 2021, 08:05
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