1. Properties of Exponents
Section 5-1

2. Objectives
I can use all exponent rules to simplify expressions.

3. Properties of Exponents
Negative Exponents
Multiplying Exponents
Dividing Exponents
Properties of Powers
Zero Exponent

4. Negative Exponents
For any real number a; and any integer n; where a  0; then the following is true:

5. Negative Exponents
You cannot have negative exponents in any of your final simplified answers.
You will use the previous rule to convert all negative exponents into positive exponents:
Ex: x-3 =

6. Multiplying Powers For any real number a; and integers m & n;
am • an = am+n
Example: x7 • x4 = x11

7. Dividing Powers For any real number a; and integers m & n;
am  an = am-n
Example: x7  x4 = x3

8. Properties of Powers
If m & n are integers, then the following hold true:
Power of a Power: (am)n = amn
Power of Product: (ab)m = ambm
Example 1: (x3)4 = x12
Example 2: (xy2)3 = x3y6

9. Zero Exponent Given any number m, where m  0 Then m0 = 1 Examples :
(-89)0 = 1

10. Using Exponent Properties to Simplify Monomials
Simplify (2x2y3)(-5x4y2)
We can write this in simplest expanded form:
(2•x • x • y • y • y)(-5 • x • x • x • x • y • y )
Using commutative property to regroup
(2 •–5)(x • x • x • x • x • x)(y • y • y • y • y)
-10 x6 y5

11. Examples 2-3 Simplify (a4)5 a20 Simplify (-5p2s4)3 (-5)3p6s12

12. GUIDED PRACTICE for Examples 1 and 2 2 3 3. 9 SOLUTION 2 3 23 = 9 93 8
2 3 9
SOLUTION
2 3 9 23 93 =
Power of a quotient property 8
729 =
Simplify and evaluate power.

13. GUIDED PRACTICE for Examples 3, 4, and 5 s 3 2 7. t–4 SOLUTION s 3 2=
Power of a product property
t–8 s6 =
Evaluate power.
s6t8 =
Negative exponent property

14. GUIDED PRACTICE for Examples 3, 4, and 5 8. x4y–2 3 x3y6 SOLUTION=
(x4)3 (y–2)3
(x3)3(y6)3
Power of a powers property =
x12y–6
x9y18
Power of a powers property
= x3y–24
Power of a Quotient property x3
y24 =
Negative exponent property

15. Simplify the expression. Tell which properties of exponents you used.
GUIDED PRACTICE
for Examples 3, 4, and 5
Simplify the expression. Tell which properties of
exponents you used.
5. x–6x5 x3
SOLUTION
x–6x5x3
= x–6x5 + 3
Power of a product property
= x2
Simplify exponents.

16. GUIDED PRACTICE for Examples 3, 4, and 5 6. (7y2z5)(y–4z–1) SOLUTION
Power of a product property
= (7y2 – 4)(z5 +(–1))
Simplify
= (7y–2)(z4)
Negative exponent property
= 7z4 y2

17. Homework
Worksheet 8-1