1. Properties of Exponents
Multiplication Property
When you multiply terms with the same base you add the exponents
xm * xn = xm+n
So as an example…
x2 * x4 = x2+4 = x6

2. Properties of Exponents
Division Property
When you divide terms with the same base you subtract the exponents (top – bottom)
xm / xn = xm-n
So as an example…
x5 * x2 = x5-2 = x3

3. Properties of Exponents
Power raised to a Power
When you have a power outside of parenthesis you multiply ALL exponents inside by the exponent outside
(xmyn)k = xm*kyk*n
So as an example…
(x5y2)4 = x5(4)y2(4) = x20y8

4. Properties of Exponents
Zero Exponents
Anything except zero raised to the zero power is equal to 1
x0 = 1
Why? x x1 = =
x1-1 x x1
But… x
We know that
So… = 1 x
x0 = 1

5. Properties of Exponents
Negative Exponents
Any time you have a negative exponent you move the term with the negative exponent to the opposite part of the fraction and make it positive 1 1 xn
x-n = = xn xn =
x-n 1

6. Homework
pg 453 #22, 27, 40, 47
pg 459 #14, 24, 34, 39
Pg 466 #31, 43, 45, 46
pg 473 – #16, 20, 27, 35

7. Scientific Notation - Expansion
Scientific Notation uses a number between 1 and 10 (but not equal to 10) that is raised to a power of 10
2.834 x 104 = (move the decimal 4 places to the right)
2.834 x 10-2 = (move the decimal 2 places to the left)

8. Scientific Notation - Contraction
42502 = x 104 (exponent means you moved the decimal 4 places to the left)
= x 10-5 (exponent means you moved the decimal 5 places to the right)

9. Practice
2x2 * 4x3
= 8x5
6x6y7
3x3
= 3x3y-2 =
2x3y9 y2

10. Practice
(2a3b2)3
8a9b6
23a9b6 = =
4a3b9
4a3b9
4a3b9 =
2a6b-3
2a6 = b3

11. Homework Answers 22) 32 * 36 = 38 27) (3 * 7)2 = 32 * 72
Keep the base the same and add the exponents
27) (3 * 7)2 =
32 * 72
Distribute the exponent to ALL exponents in the parenthesis
40) 2x3 * (3x)2
= 2x3 * 32x2
= 2x3 * 9x2
= 18x5

12. Homework Answers
47) (6a4)2 * (1/4a2)2
= 62a8 *(1/4)2a4
= 36a8 *(1/16)a4
= (36/16)a12
14) 4-2
= 4-2/1
= 1/42
24) 8-7 * 87
= (1/87) * 87
= 87/87
= 1

13. Homework Answers
34) x4y-7
= x4(1/y7)
= x4 /y7
39) (-4x)-3
= (-4)-3x-3
= 1/((-4)3x3)
= 1/(-64x3)
31) (3)4 81 = x4
(x)4

14. Homework Answers
43) 4x4y3
5xy2 * 2y
2xy
20x5y5 =
5x4y3
4xy2

15. Homework
pg 473 – #16, 20, 27, 35
pg #43, 52
pg 459 #37, 43, 44
pg 466 #42, 44, 47, 48