1. Exponential Notation
1-3

2. I. Using Exponents A. Vocabulary:
Power – product in which the factors are the same
Exponent – tells how many times the base is multiplied
Base – the number that is multiplied
Exponential notation – an expression that is written with exponents

3. B. Writing out an expression with exponential notation: 22 = 2 x 2 35 = 3 x 3 x 3 x 3 x 3 n4 = n x n x n x n y3 = y x y x y 2y3 = 2 x y x y x y (the exponent is only connected to the y, so that is the only thing that is expanded)

4. Examples:
1. 54
2. b3
3. 2x3
4. 12y4

5. C. Writing in exponential notation: 7 x 7 x 7 x 7 = 74 n x n x n x n x n x n = n6 3 x m x m = 3m2 2 x y x y x y x y = 2y4

6. Examples: 1. 9 x 9 x 9 2. y · y · y · y · y 3. 4 x n x n x n x n x n
· x · x · x · x
x b x b x b

7. You can also “evaluate” problems that include exponents
Note:
You can also “evaluate” problems that include exponents
ex. y for y = 2
24 + 3
2 · 2 · 2 · 2 + 3 =
End of Part 1

8. II. Exponents with Parentheses
Up until now, all exponents were connected to only one number/variable, known as the base
2y5
When an expression inside parentheses is raised to a power, everything inside the parentheses becomes the base
(2y)5

9. A. To solve problems with exponents on the outside of the parentheses, you must connect/distribute the exponent to everything on the inside
1. (3a) (5y)3
34 · a4
53 · y3
81 · a4
125 · y3
81a4
125y3

10. B. You can also do this same thing with evaluating:
Example:
(4m)3 for m = 2
43 · m3
43 · 23
64 · 8
512

11. Examples:
1. (10y) (6m) (8n)5 for n=2
End of Part 2

12. C. When you have exponents both inside and outside of the parentheses:
You must multiply the exponents
(52)3
56 = 15,625
Multiply your exponents

13. Examples:
1. (84) (k7) (3a2)5

14. III. Exponents in Fractions
A. If you have the same base in the top and bottom of the fraction, and they have exponents, you can simplify B. As long as they are the same base, you will take the top exponent and subtract the bottom exponent
Take the exponents and subtract…5 – 3 = 2

15. Examples:
b x
b x3

16. C. If you do not have the same base, you cannot subtract the exponents
D. If there are multiple bases, combine your like bases and leave the rest where they were
x6y2 =
x3z4
x3y2 z4
Here are your like bases… subtract the exponents

17. Examples:
a3b xy
b2c y