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I know this is very basic, but when evaluating

$\frac{b^{-4}}{b^{-4}}$

Apparently I cannot write it as $\frac{b^4}{b^4}$ by moving the expressions to make them positive. Why can't I do that? The answer is supposed to be $b^8$ not 1, like I originally thought.

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    Then it is $b^{-8}$, or $\frac{1}{b^8}$.2012-11-06

2 Answers 2

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Simply because $x/x=1$ for all non zero real numbers. $\frac {b^{-4}}{b^{-4}}$ is an expression of the form $x/x$ (assuming $b\neq0$) and so it equals $1$. One can show this using this other method: $\frac{b^{-4}}{b^{-4}}={b^{-4}}\frac1{b^{-4}}={b^{-4}}{b^{4}}=b^{-4+4}=b^0=1$

It is however $b^{-8}$ if $\dfrac{b^{-4}}{b^4}$ which can be shown using the method above.

I hope this helps.
Best wishes, $\mathcal H$akim.

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    Thanks @amWhy ! Corrected. $\overset{\cdot\cdot}\smile$2014-03-29
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Your answer is flawed. The answer is one because any number $x: x \in \mathbb{R}$ \ $0$ divided by itself equals one.

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    Sorry about that.2014-03-29