6-3: Rational 6-3: Rational ExponentsExponents

6-3: Rational 6-3: Rational ExponentsExponents

Unit 6: Rational /Radical Unit 6: Rational /Radical EquationsEquations

Recall: Exponent Rules

Rational exponents behave exactly like the whole number exponents

Let’s look at some review problems

Definition of a rational exponent

Roots of nth roots

Case Roots Example

Odd index 1 real root

Even index (positive radicand)

2 real roots

Even index (negative radicand)

No real roots

radicand of 0 1 root of 0

2=8;2=8 33

2±=164

i2±=164

0=0

Find all real roots

1. 2. 3.

4. 5. 6.

4 81 3 125 6 729

4 256 6 1 3 64

Simplifying nth roots

Recall: and The same applies here:

Ex.

nnn baab =)(n

nn

ba

ba

=)(

baab •=

3333 22=2•8=16

33 93 23 7 ==• xxxx

Definition of a rational exponent

A rational exponent is defined as:

Where m and n are integers and n ≠ 0.

Ex.

nm

n m aa =

2=16=16 441

( ) 4=2=8=8 22332

Write each expression in radical form and simplify.

Write each expression using rational exponents.

Solve.