72A Zero and Negative Exponents

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7-2A Zero and Negative Exponents
Algebra 1 Glencoe McGraw-Hill Linda
Stamper
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Inductive Reasoning is making conclusions based
on patterns you observe. Today you will use
patterns to formulate a rule for negative
exponents and for nonzero numbers to the zero
power.
Before we look at some data, identify whether the
following number is located in a numerator or a
denominator position.
What is the denominator?
3
Complete the chart.
22
20
2-4
2-3
2-2
2-1
21
23
24
The table shows 3 different ways to write the
same value!
4
Complete the chart.
22
20
2-4
2-3
2-2
2-1
21
23
24
32
30
3-4
3-3
3-2
3-1
31
33
34
5
Complete the chart.
22
20
2-4
2-3
2-2
2-1
21
23
24
32
30
3-4
3-3
3-2
3-1
31
33
34
What rule can you formulate about a nonzero
number to the zero power?
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Complete the chart.
22
20
2-4
2-3
2-2
2-1
21
23
24
32
30
3-4
3-3
3-2
3-1
31
33
34
What rule can you formulate about a nonzero
number to the zero power?
Any nonzero number to the zero power is 1.
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I am going to remove the middle row.
8
What do you notice about the exponents?
24
23
22
21
20
2-1
2-2
2-3
2-4
When exponents change position from the numerator
to the denominator (or the denominator to the
numerator), the sign of the exponent changes.
34
33
32
31
30
3-1
3-2
3-4
3-3




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Points to remember
201
A nonzero number to the zero power is 1. Zero to
the zero power is undefined! When moving a power
(base and exponent) from numerator to denominator
(or denominator to numerator), change the sign of
the exponent. A simplified expression means
positive exponents. The exponent acts on the
base and the base alone (not even on the sign of
the base, unless the sign is in parentheses!).
Copy all the above in your notebook!
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Simplify the expression.
Example 1
Example 2
Simplified means no negative exponents!
Example 3
Example 4
Rewrite power with a positive exponent move to
denominator and change sign of exponent.
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Simplify the expression.
Example 6
Example 5
12
Simplify the expression.
Example 7
Example 8
Rewrite power with positive exponent move to
denominator and change sign of exponent.
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Simplify the expression.
Example 9
Example 10
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Simplify the expression.
Example 11
Example 12
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Practice Problems. Simplify the expression.
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Homework
8-A3 Handout A3.
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Working with zero.