9/8/2015
Warm Up
R.6 part 2 – Rational Exponents
Simplify, leave no neg. exponents.
Simplify, leave
no neg. exponents.
2
x --22(x −−44) 2
1. x (−x5 )
1.
x −5
x
−6
−6
Objective: TSW evaluate rational
exponents.
3
3
2. − 5 x • 3x
2. − 5 x • 3x
What do you think?
True or False? Why?
m
a
n
1
=  a n 


m
Definition of Rational Exponents
For any nonzero number b and
any integers m and n with n > 1,
m
n
n
m
b = b =
m
( b)
n
except when b < 0 and n is even
To Simplify Expressions with Rational
Exponents:
1. Be sure the exponents are positive.
2. Rewrite in radical form.
3. Take the root of the number (square root, cube
root, fourth root, etc)
4. Then raise the new number to the power
indicated.
***The numerator is the exponent, the
denominator is the radical***
Examples: Evaluate each expression.
1.
2.
3.
1
9/8/2015
Examples: Evaluate each expression.
Example 6:
4.
5.
Example 7:
To Factor with Negative Exponents
1. Take out the lowest exponent (when you are
dealing with negatives, remember -5 is
smaller than -4. So you would factor out the
exponent of -5).
2. Once you factor out subtract exponents
inside with the exponent you took out.
3. Rewrite in factored form.
Example 8:
Example 9:
2
9/8/2015
Homework
R.6 part 2 page 60 #’s 47-61 odd, 73-83 odd
3