# How do you simplify b^5 • b^4?

Apr 24, 2016

${b}^{9}$

#### Explanation:

Notice that for a positive integer $n$, we can define:

${b}^{n} = {\overbrace{b \cdot b \cdot \ldots \cdot b}}^{\text{n times}}$

So we find:

${b}^{m} \cdot {b}^{n} = {\overbrace{b \cdot b \cdot \ldots \cdot b}}^{\text{m times" * overbrace(b * b * ... * b)^"n times}}$

$= {\overbrace{b \cdot b \cdot \ldots \cdot b}}^{\text{m + n times}}$

$= {b}^{m + n}$

So in particular:

${b}^{5} \cdot {b}^{4} = {b}^{5 + 4} = {b}^{9}$