ORCCA Exponentiation (Raising to Powers)

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:

$ 5.00 \overset{4 times}{\overset{⏞}{\cdot 2 \cdot 2 \cdot 2 \cdot 2}}

$\begin{equation*} \$5.00\overbrace{{}\cdot2\cdot2\cdot2\cdot2}^{4\text{ times}} \end{equation*}$

Rather than write so many “ ${}\cdot2\text{,}$ ” there is this notation:

$ 5.00 \cdot 2^{4}

$\begin{equation*} \$5.00\cdot2^4 \end{equation*}$

CheckpointB.5.1

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.