SectionB.5Exponentiation (Raising to Powers)
On occasion, we may need to multiply by the same number over and over again. For example, suppose we place a bet of \(\$5.00\) with the “double or nothing” rules. (So if we win, our money is doubled, but if we lose, it's all gone.) What if we won four times in a row, and after each win placed a bet with all that we had won? We'd end up with this much money:
\begin{equation*}
\$5.00\overbrace{{}\cdot2\cdot2\cdot2\cdot2}^{4\text{ times}}
\end{equation*}
Rather than write so many “\({}\cdot2\text{,}\)” there is this notation:
\begin{equation*}
\$5.00\cdot2^4
\end{equation*}
So an expression like \(2^4\) means to multiply repeatedly. The number being multiplied (in this case, \(2\)) is called the base and the number of times it is multiplied (in this case, \(4\)) is called the exponent. All together, \(2^4\) is a power (specifically, a power of \(2\)).
Check your understanding with a few exercises.
CheckpointB.5.2
Calculate each of the following by hand, then check your results.