Transcript Slide 1

7-1
7-1 Integer
IntegerExponents
Exponents
Warm Up
Lesson Presentation
Lesson Quiz
Holt
Holt
McDougal
Algebra 1Algebra
Algebra11
Holt
McDougal
7-1 Integer Exponents
Warm Up
Evaluate each expression for the given
values of the variables.
1. x3y2 for x = –1 and y = 10
2.
–100
for x = 4 and y = (–7)
Write each number as a power of the
given base.
3. 64; base 4
43
4. –27; base (–3)
Holt McDougal Algebra 1
(–3)3
7-1 Integer Exponents
Objectives
Evaluate expressions containing zero
and integer exponents.
Simplify expressions containing zero
and integer exponents.
Holt McDougal Algebra 1
7-1 Integer Exponents
You have seen positive exponents. Recall that
to simplify 32, use 3 as a factor 2 times: 32 =
3  3 = 9.
But 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
Value 3125 625 125 25
5
Holt McDougal Algebra 1
5
5
5
51
5
50
5–1
5–2
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When the exponent decreases by one, the value
of the power is divided by 5. Continue the
pattern of dividing by 5.
Holt McDougal Algebra 1
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Remember!
Base
x
4
Exponent
Holt McDougal Algebra 1
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Holt McDougal Algebra 1
7-1 Integer Exponents
Notice the phrase “nonzero number” in the
previous table. This is because 00 and 0 raised to
a negative power are both undefined. For
example, if you use the pattern given above the
table with a base of 0 instead of 5, you would
get 0º =
. Also 0–6 would be
=
. Since
division by 0 is undefined, neither value exists.
Holt McDougal Algebra 1
7-1 Integer Exponents
Reading Math
2–4 is read “2 to the negative fourth power.”
Holt McDougal Algebra 1
7-1 Integer Exponents
Example 1: Application
One cup is 2–4 gallons. Simplify this expression.
gal is equal to
Holt McDougal Algebra 1
7-1 Integer Exponents
Check It Out! Example 1
A sand fly may have a wingspan up to 5–3 m.
Simplify this expression.
5-3 m is equal to
Holt McDougal Algebra 1
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Example 2: Zero and Negative Exponents
Simplify.
A. 4–3
B. 70
7º = 1
C. (–5)–4
D. –5–4
Holt McDougal Algebra 1
Any nonzero number raised to the zero
power is 1.
7-1 Integer Exponents
Caution
In (–3)–4, the base is negative because the
negative sign is inside the parentheses. In –3–4
the base (3) is positive.
Holt McDougal Algebra 1
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Simplify.
a. 10–4
Check It Out! Example 2
b. (–2)–4
c. (–2)–5
d. –2–5
Holt McDougal Algebra 1
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Example 3A: Evaluating Expressions with Zero and
Negative Exponents
Evaluate the expression for the given value of the
variables.
x–2 for x = 4
Substitute 4 for x.
Use the definition
Holt McDougal Algebra 1
7-1 Integer Exponents
Example 3B: Evaluating Expressions with Zero and
Negative Exponents
Simplify the expression for the given values of
the variables.
–2a0b-4 for a = 5 and b = –3
Substitute 5 for a and –3 for b.
Evaluate expressions with
exponents.
Write the power in the
denominator as a product.
Simplify the denominator.
Simplify.
Holt McDougal Algebra 1
7-1 Integer Exponents
Check It Out! Example 3a
Evaluate the expression for the given value of
the variable.
p–3 for p = 4
Substitute 4 for p.
Simplify exponent.
Write the power in the
denominator as a product.
Simplify the denominator.
Holt McDougal Algebra 1
7-1 Integer Exponents
Check It Out! Example 3b
Evaluate the expression for the given values
of the variables.
for a = –2 and b = 6
Substitute –2 for a and 6 for b.
Simplify expressions with
exponents.
Write the power in the
denominator as a product.
Simplify the denominator.
2
Holt McDougal Algebra 1
Simplify.
7-1 Integer Exponents
What if you have an expression with a negative
exponent in a denominator, such as
?
or
Definition of a
negative exponent.
Substitute –8 for n.
Simplify the exponent
on the right side.
An ifexpression
that
contains exponent
negative or
zero
So
a base with
a negative
is in
a
exponents is it
not
to the
be simplified.
denominator,
is considered
equivalent to
same base with
Expressions
be exponent
rewritten with
positive
the
opposite should
(positive)
in theonly
numerator.
exponents.
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Example 4: Simplifying Expressions with Zero and
Negative Numbers
Simplify.
A. 7w–4
Holt McDougal Algebra 1
B.
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Example 4: Simplifying Expressions with Zero and
Negative Numbers
Simplify.
C.
and
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Check It Out! Example 4
Simplify.
a. 2r0m–3
rº = 1 and
b.
Holt McDougal Algebra 1
c.
.
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Lesson Quiz: Part I
1. A square foot is 3–2 square yards. Simplify this
expression.
Simplify.
2. 2–6
3. (–7)–3
4. 60
5. –112
1
–121
Holt McDougal Algebra 1
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Lesson Quiz: Part II
Evaluate each expression for the given
value(s) of the variables(s).
6. x–4 for x =10
7.
Holt McDougal Algebra 1
for a = 6 and b = 3
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Holt McDougal Algebra 1