Basic Mathematics for College Students

Expressions of the form are called exponential expressions.The base of an
exponential expression can be a number, a variable, or a combination of numbers and
variables. Some examples are:

The base is y. The exponent is 2. Read as “ysquared.”

When an exponent is 1, it is usually not written. For example, and.

Caution! Bases that contain a sign mustbe written within parentheses.

Exponent

Base

( 2 s)^3 



4  41 xx^1

Since the sign is not written within parentheses, the

base is 8. The exponent is 4. Read as “the opposite (or

the negative) of 8 to the fourth power.”

 84 (8 8  8 8)

The base is  2 s. The exponent is 3. Read as “negative

( 2 s) 2 sraised to the third power” or “negative 2scubed.”

(^3) ( 2 s)( 2 s)( 2 s)
y^2 yy
The base is 10. The exponent is 5.
(^10) Read as “10 to the fifth power.”
(^5)  10  10  10  10  10
xn
8.6 Multiplication Rules for Exponents 689
Self Check 1
Identify the base and the
exponent:
a.
b.
Now TryProblems 13 and 17
(3y)^4
3 y^4
Self Check 2
Write as an exponential
expression:
(x+ y)(x+ y)(x+ y)(x+ y)(x+ y)
Now TryProblems 25 and 29
EXAMPLE (^1) Identify the base and the exponent in each expression:
a. b. c.
StrategyTo identify the base and exponent, we will look for the form.
WHYThe exponent is the small raised number to the right of the base.
Solution
a.In , the base is 8 and the exponent is 5.
b. means. Thus, the base is , not. The exponent is 3.
c.Because of the parentheses in (7a)^3 , the base is 7 aand the exponent is 3.
7 a^37 a^3 a 7 a

85

85 7 a^3 (7a)^3

EXAMPLE (^2) Write each expression in an equivalent form using an
exponent: a.b bbb b.
StrategyWe will look for repeated factors and count the number of times each
appears.
WHYWe can use an exponent to represent repeated multiplication.
Solution
a.Since there are four repeated factors ofbinb bbb, the expression can be
written asb^4.
b.Since there are three repeated factors of in , the expression can be
written as 5 t^3.
t 5 ttt
5 ttt