Well, I can't be sure because you didn't actually show any of your work, but my best guess is that saw there was a *w* in both the numerator and denominator and cancelled them. However, that was not a mathematically valid step. The two rules of exponents needed to solve this problem are:

\(\displaystyle \dfrac{w^n}{w^m}=w^{n-m}\) and \(\displaystyle w^{-n}=\dfrac{1}{w^n}\)

Meaning that in the context of this specific problem:

\(\displaystyle \dfrac{w^9}{w^{21}}=w^{9-21}=w^{-12}=\dfrac{1}{w^{12}}\)

Now, personally I find rules and formulas, in and of themselves, to be fairly unhelpful, because such a rule or formula often very quickly becomes some magical, mystical thing you memorize and it works but you'll be darned if you know how or why. Instead, I find that a much better way to approach it is to think about what the concept really *means*, and by doing so you'll actually derive the formula or rule.

This problem deals with powers, so let's review what a power really is and what it means. Raising a number to some power is essentially just repeated multiplication. So, \(\displaystyle w^n\) is really \(\displaystyle w \cdot w \cdot w \cdot ... \cdot w\) with *n* copies of *w*. Accordingly, we can rewrite the expression in the penultimate step:

\(\displaystyle \dfrac{w^9}{w^{21}}=\dfrac{w \cdot w \cdot w \cdot w \cdot w \cdot w \cdot w \cdot w \cdot w}{w \cdot w \cdot w \cdot w \cdot w \cdot w \cdot w \cdot w \cdot w \cdot w \cdot w \cdot w \cdot w \cdot w \cdot w \cdot w \cdot w \cdot w \cdot w \cdot w \cdot w}\)

Try continuing from here. What do you get after cancel out all of the common terms? How does that relate to the given rules?