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	\textbf{Exercise Eight: Over/Under}
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Some colleges to which one might apply are the following.

$\underbrace{\text{Yale, Colby}}_\text{safety schools}\text{, Bowdoin, Wisconsin, }
\underbrace{\text{Harvard, Bates}}_\text{top choices}$\\

More on those easily forgotten exponent rules. As before, we let $m,n\in\mathbb{N}$. 
$$\frac{a^m}{a^n}=\frac{\overbrace{a\cdot a\cdot \ldots \cdot a}^{m\text{ times}}}
{\underbrace{a\cdot a\cdot \ldots \cdot a}_{n\text{ times}}}=a^{m-n}$$

$$(a^m)^n=\underbrace{(\underbrace{a\cdot a\cdot \ldots \cdot a}_{m\text{ times}})
(\underbrace{a\cdot a\cdot \ldots \cdot a}_{m\text{ times}})\dots
(\underbrace{a\cdot a\cdot \ldots \cdot a}_{m\text{ times}})}_{n\text{ times}}=a^{mn}$$

If $A$ and $B$ are finite sets, then 
$A\cap B=\emptyset\iff \overline{\overline{A}}+\overline{\overline{B}}
=\overline{\overline{A\cup B}}$\\

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