Exploring Rules Of Exponents Worksheet
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7Exploring Rules of Exponents
SE A.11A use patterns to generate the laws of exponents and apply them in
problem-solving situations.
Table 1
Product of Powers Property
Use the definition of an exponent to expand the following expressions. Then
rewrite the expanded form using exponents.
Original Product
Expanded Form
Single Power
3
2
1)
2
i2
3
4
2)
w
iw
4
3)
p
i p
2
4)
xix
(
)( )
2
4
2
5)
3
x
3
x
(
)(
)
4
2
6)
5
x y
2
x y
A. Based on the patterns you observe in the first and third columns, write a shortcut in
your own words for how to arrive at the Single Power column.
B. Using the statement you wrote, express the shortcut algebraically.
m
n
Product of Powers Property for exponents a
= ______________
ia
C. Use the rule you have written to simplify the following expressions.
Kagan Structure: Sage-N-Scribe
( )( )
21
45
1)
=_____________
d
d
(
)(
)
13
9
33
42
2)
=_____________
k g
k g
5
31
3) 2w
=_____________
i7w
(
)(
)
+
−
2
x
1
3 1
x
4)
g
g
=__________
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