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Fraction raised to a negative exponent

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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Source: — Quantitative Reasoning |
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by kstv » Thu Mar 11, 2010 6:34 am
take 1/5 = x
x ^ -2 = 1/x² = 25
any method should give u this result.
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by ceilidh.erickson » Thu Nov 30, 2017 2:42 pm
Lookingfor700GMAT wrote:Is (1/5) ^ -2 = 25? Is it correct to flip the fraction (1/5 becomes 5) then square 5 =25?
Yes, "flipping the fraction" is the same as taking the reciprocal. The reciprocal of 1/5 is 5, so (1/5)^(-2) = 5^2.
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by Brent@GMATPrepNow » Thu Nov 30, 2017 5:36 pm
in general, (x/y)^(-n) = (y/x)^n
So, for example, (2/3)^(-5) = (3/2)^5

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by Matt@VeritasPrep » Mon Dec 04, 2017 6:05 pm
You are correct! (1/x)�² = x²
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by Matt@VeritasPrep » Mon Dec 04, 2017 6:05 pm
We could prove that easily enough too!

(1/x)�² = x²

is the same as

1 = x�² * x²

is the same as

1 = x�

which is true!
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by mbawisdom » Thu Mar 01, 2018 7:22 am
Lookingfor700GMAT wrote:Is (1/5) ^ -2 = 25? Is it correct to flip the fraction (1/5 becomes 5) then square 5 =25?
Yes, you can do that. Another way to think about it is treat 1/5 as 5^-1.

(1/5)^-2
(5^-1)^-2
5^(-1*-2)
5^2
25
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