Teaching Notes 1.19: Using Integers as Bases
Raising an integer to a power poses a problem for some students. These students sometimes
identify the base of an expression incorrectly and then go on to simplify the expression
incorrectly.- Explain that (−3)^2 is not the same as− 32.
- Discuss the meaning of (−3)^2. Note that the base,−3, is in parentheses. Explain that
(−3)^2 =− 3 ×(−3)=9. Because−3 is a factor two times, the product is positive. - Discuss the meaning of− 32. Note that in this case, 3 is the base, not−3. Explain that
− 32 =−(3×3)=−9. Because both factors are positive and the negative sign refers to
the quantity, the product is−9. - Explain that two different expressions may have the same value, for example:
- (−3)^3 =− 3 ×(−3)×(−3)=−27 Because−3 is a factor three times, the product is
negative. - − 33 =−(3× 3 ×3)=−27 Because the factors are positive and the negative sign
refers to the quantity, the product is negative.
- (−3)^3 =− 3 ×(−3)×(−3)=−27 Because−3 is a factor three times, the product is
- Review the examples on the worksheet with your students. Encourage your students to pay
close attention to the base and write the problems correctly.
EXTRA HELP:
Any number, except 0, raised to the zero power is equal to 1.ANSWER KEY:
(1)− 36 (2) 36 (3) 125 (4)− 125 (5)− 125 (6)− 1 (7) 1 (8)− 1 (9)− 8 (10)− 81 (11)− 16 (12) 64
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(Challenge)Yes. Explanations may vary. One response is that an exponent shows the number
of times the base is used as a factor. If two negative numbers are multiplied, the product is
positive; if three negative numbers are multiplied, the product is negative; and so on.
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