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When exponents are equal, are bases equal too?

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When exponents are equal, are bases equal too? [#permalink] New post 20 Nov 2013, 22:53
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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?
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Magoosh GMAT Instructor
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Re: When exponents are equal, are bases equal too? [#permalink] New post 21 Nov 2013, 11:40
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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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Magoosh Test Prep

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Re: When exponents are equal, are bases equal too? [#permalink] New post 21 Nov 2013, 20:28
Expert's post
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, 20:28
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