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 with the βdouble or nothingβ 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:
Rather than write so many ββ there is this notation:
So an expression like means to multiply repeatedly. The number being multiplied (in this case, ) is called the base and the number of times it is multiplied (in this case, ) is called the exponent. All together, is a power (specifically, a power of ).
Check your understanding with a few exercises.
CheckpointB.5.2
Calculate each of the following by hand, then check your results.