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Class Opener
September 17, 2012
8
1)
Evaluate
 4n  5
n 3
2)
Write recursive and explicit formulas for the
sequence 100, 96, 92, 88, …
Short Subject – Exponents and Radicals
September 17, 2012
Complete the True-False Problems in your
groups
Be prepared to defend your reasoning
Exponents and Radicals
True or False.
1. x3x4 = x12
3. x2 + x2 = x4
5. x2 + x2 = 2x2
6. (2x2)(2x2 )= 4x2
8.
x3y3
=
(xy)3
2. (x3)4 = x12
4. x12
8
x
4
x
7. (x + y)2= x2 + y2
9.
x
x
 
4
y
 y
4
4
if y ≠ 0
The Product Rule

If a is a real number and m and n are integers,
then am • an = am + n.

Examples
1) x4 • x9
3) 54 • 37
2) x5 • x–7
4) x 3/4  x5/6
The Power Rule

If a is a real number and m and n are integers,
then (am)n = amn.

Examples
5) (x5)3
7) (y2/3)4/5
6) (x4)–2
The Quotient Rule

If a is a real number and m and n are integers,
then a m
mn
a

n
a
Examples
15
x
8) 4
x
x7
9) 7
x
x3
10) 4 5
x x
x 4/3
11) 2/5
x
Power of a Product
If x and y are real numbers and n is an integer,
then xn•yn = (xy)n.
Examples
12) (x2y3)4
13) (2x5)3
14) (–3x4)4
Power of a Quotient
If x and y are real numbers, y ≠ 0, and n is an
n
n
integer, then x  x 
 
y
 y
n
Examples
x 
15)  4 
y 
5
6
 2
16)  7 
z 
5
Negative Exponents
If a is a real number and m is an integer, then
a
m
1
 m
a
Examples – Simplify (or rewrite using no
negative exponents):
4
2 5


x
1


17) 3–2 18) 5–3 19)   20)  3 
2
y 
Upcoming Events
Homework #13 due tomorrow
(on p. 74-77 in text book)
 Memorize perfect squares,
cubes, etc.
 Chapter 2 Test on Wednesday
