Page 108 - Basic College Mathematics with Early Integers

1.9 EXPONENTS, SQUARE ROOTS, AND ORDER OF OPERATIONS Objectives

Write Repeated Factors Using
Exponential Notation.
Objective Using Exponential Notation
Evaluate Expressions Containing
# # # #
In the product 3 3 3 3 3, notice that 3 is a factor several times. When this Exponents.
happens, we can use a shorthand notation, called an exponent, to write the repeated
multiplication. Evaluate the Square Root of a
Perfect Square.
# # # #
3 3 3 3 3 can be written as
3 is a factor 5 times Use the Order of Operations.

exponent Find the Area of a Square.
3 5 Read as “three to the fifth power.”
base

This is called exponential notation. The exponent, 5, indicates how many times
the base, 3, is a factor.
The table below shows examples of reading exponential notation in words.

Expression In Words
5 2 “five to the second power” or “five squared”

5 3 “five to the third power” or “five cubed”
5 4 “five to the fourth power”

Usually, an exponent of 1 is not written, so when no exponent appears, we
1
assume that the exponent is 1. For example, 2 = 2 1 and 7 = 7 .

Examples Write using exponential notation. PRACTICE 1–4
Write using exponential
# #
1. 7 7 7 = 7 3
notation.
#
2. 3 3 = 3 2 # # #
1. 8 8 8 8
# # # #
3. 6 6 6 6 6 = 6 5 # #
2. 3 3 3
# # # # # #
4. 3 3 3 3 17 17 17 = 3 4 # 17 3 # # # #
3. 10 10 10 10 10
# # # # # # #
Work Practice 1–4 4. 5 5 4 4 4 4 4 4
Objective Evaluating Exponential Expressions
To evaluate an exponential expression, we write the expression as a product and
then find the value of the product.
PRACTICE 5–8
Examples Evaluate.
Evaluate.
2
#
5. 9 = 9 9 = 81 5. 4 2 6. 7 3
1
#
6. 6 = 6 7. 11 1 8. 2 3 2
4
# # #
7. 3 = 3 3 3 3 = 81
2
#
# #
8. 5 6 = 5 6 6 = 180
Work Practice 5–8 Answers
1. 8 4 2. 3 3 3. 10 5 4. 5 2 # 4 6
5. 16 6. 343 7. 11 8. 18
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