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negative exponents

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negative exponents

by Stockmoose16 » Tue Oct 07, 2008 2:57 pm
Can someone please explain why the following does not work out to the same answer:

(1) (1/5)^n > 25

= 5^-n > 5^2
= -n>2
=N< -2

(2) (1/5)^n>25
= (1/5)^n > (1/5)^-2
= N>-2

Why am I coming out with two different answers? They should both be the same, since all I'm doing in #1 is factoring the left side into an exponent of 5, and in #2, I'm factoring the right side into an exponent of 1/5.
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by madeline » Tue Oct 07, 2008 5:32 pm
(1/5)^n > (1/5)^-2
= N>-2
This step in (2) is wrong. If (1/5)^n > (1/5)^m, then n<m. This is true for all numbers between 0 and 1 (such as 1/5).

Consider the following:

(1/5)^-3 = 5^3 = 125
(1/5)^-2 = 5^2 = 25
...
(1/5)^2 = 1/25
(1/5)^3 = 1/125

So the greater the power, the smaller your result.

Hence, if (1/5)^n > (1/5)^m, then m must be greater than n.
Therefore:
(1/5)^n > (1/5)^-2
=> n<-2

Hope that helped!
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