# Thread: Negative exponent flipping question

1. ## Negative exponent flipping question

Hello all!

I'm preparing for an Algebra test on Monday. I understand that $\displaystyle (2)^{-3} = \frac {1}{2^3}$ ultimately resulting in $\displaystyle \frac{1}{8}$ and I understand "why." Our teacher gave me a really good explanation starting with $\displaystyle (2)^{0}=1$ and worked down from there, I finally got it!

But what I don't seem to understand is why, $\displaystyle \Big( \frac{2}{z}\Big)^{-3}=\frac{z^3}{8}$. If I had to break it down I would start with, $\displaystyle \Big( \frac{2}{z}\Big)^{-3} = \Big( \frac{{2^{-3}}}{{z^{-3}}} \Big)$ but I get lost after that because I don't really understand why the exponents subtract from each other (or add) and why.

Do the -3 cancel each other out? (e.g, -3(+3)) that would result in 0.

So what exactly happens when they flip?

Thank you

2. ## Re: Negative exponent flipping question

(2/x)^(-3) = 1 / (2/z)^3 = 1 / (8/z^3) ..... HOKAY?

3. ## Re: Negative exponent flipping question

Originally Posted by alexcordero
Hello all!

I'm preparing for an Algebra test on Monday. I understand that $\displaystyle (2)^{-3} = \frac {1}{2^3}$ ultimately resulting in $\displaystyle \frac{1}{8}$ and I understand "why." Our teacher gave me a really good explanation starting with $\displaystyle (2)^{0}=1$ and worked down from there, I finally got it!

But what I don't seem to understand is why, $\displaystyle \Big( \frac{2}{z}\Big)^{-3}=\frac{z^3}{8}$. If I had to break it down I would start with, $\displaystyle \Big( \frac{2}{z}\Big)^{-3} = \Big( \frac{{2^{-3}}}{{z^{-3}}} \Big)$
Good! So you have $\displaystyle \frac{\frac{1}{8}}{\frac{1}{z^3}}$. Now some time ago you surely learned that "to divide fractions, invert the divisor and multiply". So $\displaystyle \frac{\frac{1}{8}}{\frac{1}{z^3}}= \frac{1}{8}\frac{z^3}{1}= \frac{z^3}{8}$.

but I get lost after that because I don't really understand why the exponents subtract from each other (or add) and why.

Do the -3 cancel each other out? (e.g, -3(+3)) that would result in 0.
$\displaystyle (a^x)(a^y)= a^{x+y}$ only for the same base, a. Here you have $\displaystyle z^3$ and $\displaystyle 2^3$. The bases are different so you cannot combine exponents.

So what exactly happens when they flip?

Thank you