\displaystyle [br]\begin{equation*} a^b \times a^c = \underbrace{a \times a \times \cdots a}_{b \, \text{times}} \times \underbrace{a \times a \times \cdots a}_{c \,\text{times}} = \underbrace{a \times a \times \cdots a}_{(b+c) \, \text{times}} = a^{b+c}\end{equation*}
\displaystyle [br]\begin{equation*} a^b \times a^c = \underbrace{a \times a \times \cdots a}_{b \, \text{times}} \times \underbrace{a \times a \times \cdots a}_{c \,\text{times}} = \underbrace{a \times a \times \cdots a}_{(b+c) \, \text{times}} = a^{b+c}\end{equation*}
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