6-3: rational exponents unit 6: rational /radical equations
TRANSCRIPT
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.