Transcript Integer Exponents PowerPoint integer_exponents

7-1
7-1 Integer
IntegerExponents
Exponents
Warm Up
Lesson Presentation
Lesson Quiz
Holt
Algebra
Holt
Algebra
11
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 Algebra 1
(–3)3
7-1 Integer Exponents
Objectives
Evaluate expressions containing zero
and integer exponents.
Simplify expressions containing zero
and integer exponents.
Holt 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 Algebra 1
5
5
5
51
5
50
5–1
5–2
7-1 Integer Exponents
When the exponent decreases by one, the value
of the power is divided by 5. Continue the
pattern of dividing by 5.
Holt Algebra 1
7-1 Integer Exponents
Remember!
Base
x
4
Exponent
Holt Algebra 1
7-1 Integer Exponents
Holt Algebra 1
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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 Algebra 1
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Reading Math
2–4 is read “2 to the negative fourth power.”
Holt Algebra 1
7-1 Integer Exponents
Example 1: Application
One cup is 2–4 gallons. Simplify this expression.
cup is equal to
Holt 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 Algebra 1
7-1 Integer Exponents
Example 2: Zero and Negative Exponents
Simplify.
A. 4–3
B. 70
7º = 1
C. (–5)–4
D. –5–4
Holt 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 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 Algebra 1
7-1 Integer Exponents
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 Algebra 1
7-1 Integer Exponents
Example 3B: Evaluating Expressions with Zero and
Negative Exponents
Evaluate 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.
Evaluate the powers in
the product.
Simplify.
Holt 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.
Evaluate exponent.
Write the power in the
denominator as a product.
Evaluate the powers in
the product.
Holt 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.
Evaluate expressions with
exponents.
2
Holt Algebra 1
Write the power in the
denominator as a product.
Evaluate the powers in
the product.
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.
Holt Algebra 1
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Example 4: Simplifying Expressions with Zero and
Negative Numbers
Simplify.
A. 7w–4
Holt Algebra 1
B.
7-1 Integer Exponents
Example 4: Simplifying Expressions with Zero and
Negative Numbers
Simplify.
C.
and
Holt Algebra 1
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Check It Out! Example 4
Simplify.
a. 2r0m–3
rº = 1 and
b.
Holt 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
Holt Algebra 1
1
–121
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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 Algebra 1
for a = 6 and b = 3