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Fraction exponents

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alvintom
 Post subject: Fraction exponents
 Post Posted: Sun Sep 25, 2011 3:38 am 
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Students


Posts: 5
I have a question on fraction exponents. An example

What is (25)^(3/2)?

If I split, this could be written as
(√25)^3 = +125 or -125.
=> 2 solutions

However if I could also solve it as
(5^2)^(3/2) = (5)^(2*3/2) = 5^3 = 125
=>unique solution

How to explain this anomaly and which approach should I take when solving for such expressions in GMAT?
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jnelson0612
 Post subject: Re: Fraction exponents
 Post Posted: Sat Oct 15, 2011 10:13 pm 
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ManhattanGMAT Staff


Posts: 1857
alvintom wrote:
I have a question on fraction exponents. An example

What is (25)^(3/2)?

If I split, this could be written as
(√25)^3 = +125 or -125.
=> 2 solutions

However if I could also solve it as
(5^2)^(3/2) = (5)^(2*3/2) = 5^3 = 125
=>unique solution

How to explain this anomaly and which approach should I take when solving for such expressions in GMAT?


I think it would be positive 125 only, because when taking the square root of 25 on the GMAT the GMAT test writers want you to ONLY take the positive root. Thus the square root of 25 is positive 5 only, which cubed is 125. Good question!

_________________
Jamie Nelson
ManhattanGMAT Instructor
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