# 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: 5

^{3}, x

^{-5}

• Possible to have rational (i.e. fractional )

exponents

– Ex: 8

^{1/3}, y

^{-3/4}

**Rational Exponents vs Radical**

Notation

• Relationship between rational exponents and

Notation

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

rational exponents as positive rational

exponents

•

**To evaluate rational exponents:**

– Convert to radical notation and simplify if

possible

**Simplifying Rational Exponents**

(Example)

(Example)

__ Ex 1:__ Convert to radical notation and

simplify:

**Simplifying Rational Exponent**

Expressions

• Exponent rules for integer exponents

Expressions

apply to rational exponents as well

– Remember them?

• Product : x

^{a}· x

^{b}= x

^{a+b}

• Quotient: x

^{a}/ x

^{b}= x

^{a-b}

• Power : (x

^{a})

^{b}= x

^{ab}

__Simplify – leave NO negative__

**Ex 2:**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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