Teaching Notes 6.2: Using the Properties of Exponents That
Apply to Division
To accurately simplify expressions, students may need to use the properties of exponents for
division. Students often forget these properties and simplify expressions incorrectly.- Discuss the basic steps for simplifying expressions with exponents. For example, explain that
23 = 2 · 2 · 2 =8. Emphasize that 2 is the base and 3 is the exponent. The exponent 3 means
that the base is multiplied by itself three times. - Explain that there are two properties for working with exponents and division: the property
of exponents for division and the property of exponents for a power of a quotient. - Review the properties and examples on the worksheet with your students. Be sure that they
understand how and when to apply these properties. Note that in the property of exponents
for division, the base is the same and students must subtract the exponent of the base in
the denominator from the exponent of the base in the numerator. Note that in the property
of exponents for a power of a quotient, the bases are different and the exponent applies to
the bases in both the numerator and denominator. Caution your students to be particularly
careful with negative exponents.
EXTRA HELP:
When dividing powers that have the same base, always subtract the exponent of the denominator
from the exponent of the numerator.ANSWER KEY:
(1)33
43
=
27
64
(2)
14
44
=
1
256
(3) 21 = 2 (4) 3 −^2 =
1
32
=
1
9
(5)
5 −^2
6 −^2
=
62
52
=
36
25
(6) 5 −^1 =
1
51
=
1
5
(7) 8 −^1 =
1
81
=
1
8
(8) 3 −^6 =
1
36
=
1
729
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(Challenge)Francine and Phil are both correct. They used different procedures to get the
same answer.
--------------------------------------------------------------------------------------226 THE ALGEBRA TEACHER’S GUIDE