### 7.4.2 Simplification

This subsection is not completed yet, but in the meantime here are some practice questions.

Remember:
You can cancel common factors from the top and bottom of fractions: $\frac{ab}{ac} = \frac{b}{c}$ What we’re really doing is dividing the top and bottom by $a$. Note that this only works for common factors. You can’t cancel common terms: $\frac{a + b}{a + c}\ne \frac{b}{c}$

Remember:
If after cancelling there’s nothing left in the numerator, it becomes $1$: $\frac{a}{ab} = \frac{1}{b}$ because when we divide $a$ by $a$, we get $1$. A common mistake is to make the numerator disappear, but this is wrong: $\frac{a}{ab} \ne b$

Remember:
Subtract the smaller exponent from the larger exponent when simplifying fractions: \begin{align*} \frac{a^m b}{a^n c} &= \frac{a^{m-n} b}{c}\\ \frac{a^n b}{a^m c} &= \frac{b}{a^{m-n}c} \end{align*} if $m\gt n$. We’re dividing both top and bottom of the fraction by $a^n$.