Sect 5.1 - Exponents: Multiplying And Dividing Common Bases Worksheet With Answers

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Sect 5.1 - Exponents: Multiplying and Dividing
Common Bases
Concept #1
Review of Exponential Notation
5
In the exponential expression 4
, 4 is called the base and 5 is called the
exponent. This says that there are five factors of four being multiplied
together. In expanded form, this is equal to 4 • 4 • 4 • 4 • 4. In general, if n is a
n
positive integer, then a
means that there are n factors of a being
multiplied together.
Definition
Let a be a real number and n be a positive integer. Then
n
= a • a • a • a • a ... • a
a
a is the base & n is the exponent or power.
n factors of a
Note, some books use a natural number instead of a positive integer, but a
positive integer is the same as a natural number. In this section, we will
expand the use of the exponential notation to include the use of variables
and develop some rules for simplifying variable expressions involving
exponents.
Write the following in expanded form:
7
3
Ex. 1a
x
Ex. 1b
(r – 8)
4
4
Ex. 1c
(– 7t)
Ex. 1d
– 7t
Solution:
7
= x • x • x • x • x • x • x.
a)
The base is x, and the power is 7, so x
3
b)
The base is (r – 8) and the power is 3, so (r – 8)
= (r – 8) • (r – 8) • (r – 8).
4
c)
The base is (– 7t) and the power is 4, so (– 7t)
= (– 7t) • (– 7t) • (– 7t) • (– 7t).
4
= – 7t • t • t • t.
d)
The base is t and the power is 4, so – 7t
Concept #2
Evaluating Expressions with Exponents
Simplify the following:
2
2
Ex. 2a
(– 4)
Ex. 2b
– 4
3
3
Ex. 2c
(– 0.5)
Ex. 2d
– 0.5

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