Transcript Slide 1

Rational Exponents
MATH 018
Combined Algebra
S. Rook
Overview
• Section 10.2 in the textbook:
– Simplifying rational exponents
– Simplifying rational exponent expressions
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Simplifying Rational
Exponents
Rational Exponents
• Thus far, we have only seen integer
exponents
– e.g. 53, x-5
• Possible to have rational (i.e. fractional)
exponents
1/3
– e.g. 8 , y
-3/4
4
Rational Exponents vs Radical
Notation
• A relationship exists between rational
exponents and radical notation:
p where p is the power and r is
p r
r
x  x
the radical index
• When evaluating a rational exponent, mostly
it is easier to write using radical notation
 
– e.g. Evaluate
41 2
• Most calculators take only up to the third root
– How would we evaluate
4
625
• Often helpful to write any negative rational
exponents as positive rational exponents
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Simplifying Rational Exponents
(Example)
Ex 1: Convert to radical notation and
simplify:
a)  49
1
b) 32
2
d) 16
2
8
c)  64
4
2
1
e)
5
1
 53
3
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Simplifying Rational Exponent
Expressions
Simplifying Rational Exponent
Expressions
• Exponent rules for integer exponents
apply to rational exponents as well
– Remember them?
• Product: xa ∙ xb = xa+b
• Quotient: xa / xb = xa-b
• Power: (xa)b = xab
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Simplifying Rational Exponent
Expressions (Example)
Ex 2: Simplify – leave NO negative
exponents:
 
a) a b  a 3 b

4
5
2
6
5



1
4
x
y
b)  3 1
x 8y 2
1
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Simplifying Rational Exponent
Expressions (Example)
Ex 3: Use rational exponents to simplify the
following into one radical :
a)
5
x  x
b)
4
y 5 y
3
5
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Summary
• After studying these slides, you should know
how to do the following:
– Simplify rational exponents
– Simplify rational expressions using the exponent rules
• Additional Practice
– See the list of suggested problems for 10.2
• Next lesson
– Simplifying Radical Expressions (Section 10.3)
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