1. Multiplication and Division Properties of Exponents

2. Exponent Vocabulary an = a • a • a…..a n times
Base number: the number being multiplied.
a is the base number.
Power: the number of times the base is multiplied.
n is the power.

3. Multiplication with the same base: am • an = am+n add exponents
Rules for multiplying with exponents when you have the SAME BASE!
PRODUCT OF
POWERS PROPERTY
Multiplication with the same base:
am • an = am+n add exponents
x4 • x7 = x11 add exponents

4. POWER OF POWER PROPERTY
Powers of powers with the same base:
(am)n = amn multiply exponents
(z4)3 = z12 multiply exponents

5. Power of a Product Property
Different bases, distribute power to each base and multiply.
Examples:
(a • b)4 = a4 • b4 = a4b4
(-3x)2 = (-3) 2• x 2 = 9x2

6. am Subtract exponents = am-n an g13 Subtract exponents = g10 g3
Rules for Division
QUOTIENT OF
POWERS PROPERTY
Division with the same base am an
Subtract exponents
= am-n
g13 g3
Subtract exponents
= g10

7. Power of Quotient Property
Rules for Division
Power of Quotient Property
Distribute power across the ( ) a b m am bm = w k 4 w4 k4 = x2 x 3 x6 x2 x3 = =

8. Try these!
Simplify:
69 = 10,077,696
1011 = 100,000,000,000
3. (2x) [(5x)3]6
(5x)18 = 5 18 x18
23x3 = 8x3

9. Practice 1. 2. 3. 37 34
= 33
= 27
828 85 = =
= 8-2 = 3 2 = =

10. 3y2(2y)3 (r2st3)2(s4t)3 3y2 23y3 = r4s2t6s12t3 = 3 23y5 = r4s14t9
Some final exponent practice problems…
3y2(2y)3 (r2st3)2(s4t)3
3y2 23y3
= 3 23y5
=24y5
= r4s2t6s12t3
= r4s14t9

11. Try the Challenge Problem
16x3y ∙ -2xy
-4xy x
Multiply straight across to make one fraction.
-32x4y2
4x2y3
Divide whole numbers
-8x4y2
x2y3
Subtract exponents and make sure all exponents in your answer are positive.
-8x2 y