Download 1. Simplify expressions containing zero and integer exponents

Day 1
Integer Exponents
LEARNING GOALS
1. Simplify expressions containing zero and
integer exponents (including negatives)
2. Evaluate expressions containing zero and
integer exponents (including negatives).
Holt Algebra 2
Day 1
Integer Exponents
What does 3 2 mean?
Generally exponents tell us to Multiply.
An exponent tells you how may times you are going to use the base by itself.
What does it mean for an exponent to be negative or 0?
You can use a table and look for a pattern to figure it out.
Power
55
54
53
52
51
Value
3125
625
125
25
5
50
5–1
5–2
What’s up with 0?
Caution
Can you divide by 0? ______
Why can’t we take 0 to a negative exponent then?
In (–3)–4, the base is negative because the negative sign is inside
the parentheses. In –3–4 the base (3) is positive.
Holt Algebra 2
Day 1
Integer Exponents
Words
Zero Exponents:
Integer Exponents
Numbers
Algebra
If x ≠ 0
Any number raised to the
0 power = 1
EXCEPT Zero
Negative Exponents:
Any number raised to a
negative power = 1
over the positive version
of that exponent and
base
EXCEPT Zero
Holt Algebra 2
If x ≠ 0
Day 1
Integer Exponents
Example 1: Application
A. One cup is 2–4 gallons. Simplify this expression.
B. A sand fly may have a wingspan up to 5–3 m. Simplify this expression.
Example 2: Zero and Negative Exponents
Simplify.
A. 4–3
B. 70
C. (–5)–4
a. 10–4
Holt Algebra 2
b. (–2)–4
c. (–2)–5
D. –5–4
d. –2–5
Day 1
Integer Exponents
Example 3A: Evaluating Expressions with Zero and Negative Exponents
Evaluate the expression for the given value of the variables.
A. x–2 for x = 4
a.
p–3 for p = 4
Holt Algebra 2
B. –2a0b-4 for a = 5 and b = –3
b.
for a = –2 and b = 6
Day 1
Integer Exponents
An expression that contains negative or zero exponents is not considered to be
simplified. Expressions should be rewritten with only positive exponents.
What if you have an expression with a negative exponent in a denominator, such
as 1
?
x −n
Example 4: Simplifying Expressions with Zero and Negative Numbers
Simplify.
A.
7w
−4
B.
−5
−2
k
0 −2
ab
C. −3 6
c d
4
−3
a.
0
2r m
Holt Algebra 2
−3
b.
r
7
c.
g
h −6