Rational Exponents Worksheet
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2
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4DeSmet - Math 152
Blitzer 5E
∫
- Rational Exponents
7.2
*Note: From here on out, we will assume ALL variables are positive, i.e., no more absolute values! You will
have slightly different answers in your HW from the book.
1. Remember your exponent rules?
( )
( )
n
m
=
=
=
m
xy
m
n
x
x
x
m
⎛
⎞
x
=
− m
=
=
0
⎝ ⎜
⎠ ⎟
x
x
y
− n
⎛
⎞
m
1
x
x
=
⎝ ⎜
⎠ ⎟
− m
n
x
x
y
2. We have used these rules for m and n integers. These rules NEED to hold for rational (fractional)
numbers as well!
3. Rational Exponents
What would it mean to raise 3 to the 1/2?
⋅ 3
=
1/2
1/2
3
⋅ 5
⋅ 5
=
1/ 3
1/ 3
1/ 3
5
⋅ 2
⋅ 2
⋅ 2
⋅ 2
⋅ 2
⋅ 2
⋅ 2
=
1/8
1/8
1/8
1/8
1/8
1/8
1/8
1/8
2
1
1
1
⋅ a
⋅ ⋅ ⋅ a
=
a
n
n
n
n − times
1
Thus for x a real number and n a natural number greater than 1,
can be written:
x
n
Section 7.2!
pg. 1
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