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# When exponents are equal, are bases equal too?

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Manager
Joined: 11 Sep 2012
Posts: 91
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Kudos [?]: 23 [1] , given: 9

When exponents are equal, are bases equal too? [#permalink]

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20 Nov 2013, 23:53
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When exponents are equivalent, are bases equal?

E.g. x and y are not 0 or 1

If x^3a = y^3a, is x = y?
Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4028
Followers: 1415

Kudos [?]: 6749 [0], given: 84

Re: When exponents are equal, are bases equal too? [#permalink]

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21 Nov 2013, 12:40
bschoolaspirant9 wrote:
When exponents are equivalent, are bases equal?

E.g. x and y are not 0 or 1

If x^3a = y^3a, is x = y?

Dear bschoolaspirant9,
I'm happy to help.

First of all, I believe what you mean is
x^(3a) = y^(3a)
See:
http://magoosh.com/gmat/2013/gmat-quant ... g-symbols/

The answer to your question is --- it depends. If the exponent (here, 3a) is an even number, then x and y could have equal absolute values but opposite signs.

For example,
x^2 = y^2
could mean that x = y or that x = -y. There's no way to tell from that starting equation which one is true.

If the exponent is an odd integer, then x = y --- that would be unambiguously clear.

Does this make sense?
Mike
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Mike McGarry
Magoosh Test Prep

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Re: When exponents are equal, are bases equal too? [#permalink]

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21 Nov 2013, 21:28
bschoolaspirant9 wrote:
When exponents are equivalent, are bases equal?

E.g. x and y are not 0 or 1

If x^3a = y^3a, is x = y?

To put it simply, given $$x^2 = y^2$$, can you say that x = y? Recall that all we can say is |x| = |y|, not x = y
What about given $$x^3 = y^3$$? Here x = y
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Re: When exponents are equal, are bases equal too?   [#permalink] 21 Nov 2013, 21:28
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# When exponents are equal, are bases equal too?

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