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4 Exponentiation
This chapter presents a detailed discussion of exponents. Working effi ciently
and accurately with exponents will serve you well in algebra.
Exponents
An exponent is a small raised number written to the upper right of a quantity,
which is called the base for the exponent. For example, consider the product
33333333333 , in which the same number is repeated as a factor multiple times.
The shortened notation for 33333333333 is 35. This representation of the product
is an exponential expression. The number 3 is the base, and the small 5 to the
upper right of 3 is the exponent. Most commonly, the exponential expression 35
is read as “three to the fi fth.” Other ways you might read 35 are “three to the
fi fth power” or “three raised to the fi fth power.” In general, xa is “x to the ath,”
“x to the ath power,” or “x raised to the ath power.”
Exponentiation is the act of evaluating an
exponential expression, xa.
The result you get is the ath power of the
base. For instance, to evaluate 35 , which has
the natural number 5 as an exponent, perform
the multiplication as shown here (see Figure 4.1).
Step 1. Write 35 in product form.
35 = 33333333333
Exponentiation is a big word, but it just
means that you do to the base what the
exponent tells you to do to it.
