Teaching Notes 6.1: Using Zero and Negative Numbers
as Exponents
Students often find using zero and negative numbers as exponents confusing. Negative exponents
are particularly troublesome because students seldom connect negative numbers with reciprocals.- Depending on the abilities of your students, you may want to begin with a review of expo-
nents. Explain that an exponent is the number of times the base is used as a factor. You
might want to provide an example, such as 2^3 = 2 × 2 × 2 =8. - To help your students discover how zero and negative numbers are used as exponents,
present the example of 2n. Have your students evaluate the expression whenn=3, 2, and- The answers are 8, 4, and 2. Note that each number is half of the previous term. Therefore,
the next term is 2^0 =1. Using the same reasoning, 2−^1 =
- The answers are 8, 4, and 2. Note that each number is half of the previous term. Therefore,
1
2
and 2−^2 =1
22
=
1
4
,andsoon.- Review the table, definitions, and examples on the worksheet with your students. Discuss
the definitions of zero and negative exponents. Especially note the meaning of the negative
exponent in the base of the denominator in the last example.
EXTRA HELP:
Pay close attention to the base. If the base is a negative number, the base must be written in
parentheses.ANSWER KEY:
(1)1
52
=
1
25
(2) 1 (3)
1
(−3)^4
=
1
81
(4)−
1
34
=−
1
81
(5) 1 (6) 72 = 49
(7)−
1
42
=−
1
16
(8)
1
(−4)^2
=
1
16
(9)
8
3
(10) 62 = 36 (11)
1
(−2)^3
=
1
− 8
(12)
1
23
=
1
8
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(Challenge)They are different expressions and have different values.− 50 =−1and(−5)^0 = 1
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