Integer Exponents

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Integer Exponents
Warm Up
Lesson Presentation
Lesson Quiz
Holt Algebra 1
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Warm Up Evaluate each expression for the given
values of the variables. 1. x3y2 for x 1 and
y 10 2. for x 4 and y (7) Write each
number as a power of the given base.
100
3. 64 base 4
43
4. 27 base (3)
(3)3
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Objectives
Evaluate expressions containing zero and integer
exponents. Simplify expressions containing zero
and integer exponents.
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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
Value
55
54
53
52
51
51
50
52
625
3125
125
25
5
5
When the exponent decreases by one, the value of
the power is divided by 5. Continue the pattern
of dividing by 5.
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4
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Example 1 Application
One cup is 24 gallons. Simplify this expression.
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Check It Out! Example 1
A sand fly may have a wingspan up to 53 m.
Simplify this expression.
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Example 2 Zero and Negative Exponents
Simplify.
A. 43
B. 70
Any nonzero number raised to the zero power is 1.
7º 1
C. (5)4
D. 54
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Check It Out! Example 2
Simplify.
a. 104
b. (2)4
c. (2)5
d. 25
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Example 3A Evaluating Expressions with Zero and
Negative Exponents
Evaluate the expression for the given value of
the variables.
x2 for x 4
Substitute 4 for x.
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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.
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Check It Out! Example 3a
Evaluate the expression for the given value of
the variable.
p3 for p 4
Substitute 4 for p.
Evaluate exponent.
Write the power in the denominator as a product.
Evaluate the powers in the product.
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Check It Out! Example 3b
Evaluate the expression for the given values of
the variables.
Substitute 2 for a and 6 for b.
Evaluate expressions with exponents.
Write the power in the denominator as a product.
Evaluate the powers in the product.
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Simplify.
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Definition of a negative exponent.
Substitute 8 for n.
Simplify the exponent on the right side.
An expression that contains negative or zero
exponents is not considered to be simplified.
Expressions should be rewritten with only
positive exponents.
So if a base with a negative exponent is in a
denominator, it is equivalent to the same base
with the opposite (positive) exponent in the
numerator.
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Example 4 Simplifying Expressions with Zero and
Negative Numbers
Simplify.
A. 7w4
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Example 4 Simplifying Expressions with Zero and
Negative Numbers
Simplify.
C.
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Check It Out! Example 4
Simplify.
a. 2r0m3
b.
c.
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Lesson Quiz Part I
1. A square foot is 32 square yards. Simplify
this expression. Simplify. 2. 26 3. (7)3
4. 60
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5. 112
121
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Lesson Quiz Part II
Evaluate each expression for the given value(s)
of the variables(s).
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x4 for x 10