Teaching Notes 6.3: Using the Properties of Exponents That
Apply to Multiplication and Division
There are five different properties for working with exponents. Confusion arises when students are
asked to apply several properties to evaluate one expression. A review of the properties is helpful.- Explain that several properties for exponents may be applied to evaluate an expression. It is
important to know when to apply each one. - Review the properties and examples on the worksheet with your students. Share the follow-
ing tips:- Multiplication:Add the exponents if the bases are the same.
- Power of a power:Multiply the exponents.
- Power of a product:Raise each base of the product to the power.
- Division:Subtract the exponent of the base in the denominator from the exponent of the
base in the numerator, provided the bases are the same. - Power of a quotient:Raise each base of the quotient to the power.
EXTRA HELP:
If there are several operations in the same problem, follow the order of operations.ANSWER KEY:
(1) 26 = 64 (2) 2 −^2 =^1
4(3)
53
53
= 1 (4) 6 −^2 =^1
36
(5) 53 · 23 = 125 · 8 =1, 000 (6) 75 =16, 807 (7)
23
53
=
8
125
(8)
36 · 23
53
=
729 · 8
125
=
5, 832
125
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(Challenge)Both are correct. They used a correct property and followed the correct proce-
------------------------------------------------------------------------------------------dures. If both expressions were expressed in simplest form, both would equal 576.228 THE ALGEBRA TEACHER’S GUIDE