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Date: ____________
Lesson 3 - Working with Rational Exponents
Rational Number: a number that can be expressed as the ratio of two
integers, where the divisor is not zero
A. In general: a
1
n
 n a , for a  0
n
(where n is a natural number)
a is called a radical and means the nth root of a
We can write an expression in exponential form or radical form:
2
1
5
5
Exponential Form
B. Recall power to a power rule :
2
Radical Form
a  (a )  (a )
xy
x
y
y
x
This will help us with the more complicated radical exponents
, where m and n are natural numbers
Examples:
1. Write in radical form and solve:
a) x
1
3
b) 49
1
2
1
c) 64 3
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1
1
d)   27 3
g) 4
1
e) y 2
f) (2 x) 4
3
2
2. Write using exponential form:
a)
101
b)
5
c)
10
3
10 5
3. Evaluate:
4
1
b)  8 3
a) (8) 3
c) (8 x )
6
2
3
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Rule
Example
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