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Exponents question

I have a question on this exponents quant comparison question.

Quant A: (5^x)/(5^(x-1))
Quant B: (5^(x-1))/(5^(x-2))

x>0

The answer is that two quantities are equal.

I understand that A: 5^(x-x+1)=5 and B: 5^(x-1-x+2)=5, thus A and B are equal, but what about the case where x=1?
Then A would be 5 over zero, and B would be zero over 1/5. In this case, A and B are not equal. So should the relationship be indeterminable?

Author

Stella Yoh

Posted Nov 24, 2015

1 Explanation

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Cydney Seigerman, Magoosh Tutor

Hi Stella :) When dealing with exponents, it's important to remember that n^0 ? 0. Rather n^0 = 1. So, in this problem, when x = 1, we have:

Quant A: 5^1/5^0 = 5/1 = 5
Quant B: 5^0/5^(-1) = 1/5^(-1) = 5

We don't have to worry about zero in the denominator, and we're able to see that the two quantities are equal :)

For a more in-depth look at the properties of exponents, I definitely recommend this post on our GMAT blog: http://magoosh.com/gmat/2012/exponent-properties-on-the-gmat/

I hope this helps :)

Nov 29, 2015 • Comment