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Rational Exponents

Overview
• Section 10.2 in the textbook:
Simplifying rational exponents
Simplifying rational exponent expressions

Simplifying Rational
Exponents

Rational Exponents
• Thus far, we have only seen integer
exponents
– Ex: 53, x-5
• Possible to have rational (i.e. fractional )
exponents
– Ex: 81/3, y-3/4

Rational Exponents vs Radical
Notation
• Relationship between rational exponents and
radical notation
where p is the power and r is
the radical index
Ex:
• Most calculators take only up to the third root
– How would we evaluate

More on Rational Exponents
• Often helpful to write any negative
rational exponents as positive rational
exponents

To evaluate rational exponents:
Convert to radical notation and simplify if
possible

Simplifying Rational Exponents
(Example)

Ex 1: Convert to radical notation and
simplify:


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

Ex 2: Simplify – leave NO negative
exponents:

Ex 3: Use rational exponents to simplify the
following – leave the final answer in radical
notation:

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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