Exploring Rules Of Exponents Worksheet Page 3
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2
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4
5
6
7Table 3
Power of a Product/Quotient Property
Use the definition of an exponent to expand the following expressions. Then
rewrite the expanded form using exponents.
Original
Expanded Form
Product/Quotient
Product/Quotient
of Powers
( )
4
1)
2x
(
)
3
−
2)
4a
( )
5
3
3)
h t
2
⎛ ⎞
2
4)
⎜ ⎟
⎝ ⎠
5
3
⎛
⎞
3
5)
⎜
⎟
2
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 Product of Powers/Quotients column.
B. Using the statement you wrote, write the shortcut algebraically.
( )
m
=
Power of a Product Property for exponents
______________
ab
m
⎛ ⎞
a
Power of a Quotient Property for exponents
=______________
⎜ ⎟
⎝ ⎠
b
C. Use the rule you have written to simplify the following expressions.
( )
4
5
1)
=________
3x
(
)
6
−
5
2)
=________
2x
2
⎛
⎞
4
3x
3)
=__________
⎜
⎟
y
⎝
⎠
(
)
2
2
3
4)
3u w
=________________
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