1. Exponents

2. Location of Exponent
An exponent is a little number high and to the right of a regular or base number. 3 4
Exponent
Base

3. Definition of Exponent
An exponent tells how many times a number is multiplied by itself. 3 4
Exponent
Base

4. What an Exponent Represents
An exponent tells how many times a number is multiplied by itself. 4
= 3 x 3 x 3 x 3 3

5. How to read an Exponent
This exponent is read three to the fourth power. 3 4
Exponent
Base

6. How to read an Exponent
This exponent is read three to the 2nd power or three squared. 3 2
Exponent
Base

7. How to read an Exponent
This exponent is read three to the 3rd power or three cubed. 3 3
Exponent
Base

8. What is the Exponent? 3
2 x 2 x 2 = 2

9. What is the Exponent? 2
3 x 3 = 3

10. What is the Exponent? 4
5 x 5 x 5 x 5 = 5

11. What is the Base and the Exponent?4
8 x 8 x 8 x 8 = 8

12. What is the Base and the Exponent?5
7 x 7 x 7 x 7 x 7 = 7

13. What is the Base and the Exponent?9 2

14. How to Multiply Out an Exponent to Find the Standard Form4 3
= 3 x 3 x 3 x 3 9 27 81

15. What is the Base and Exponent in Standard Form?2 4 16 =

16. What is the Base and Exponent in Standard Form?3 2 8 =

17. What is the Base and Exponent in Standard Form?2 3 9 =

18. What is the Base and Exponent in Standard Form?3 5
125 =

19. There are many types of exponent laws...
Negative exponent law.
Quotient Law.
The Zero exponent law.
There's a product law.
And last but not least...
Power of a power.

20. Product law:
NOTE:
Ex:
add the exponents together when multiplying the powers with the same base.
This operation can only be done if the base is the same!

21. Quotient law
NOTE:
Ex:
This operation can only be done if the base is the same!
subtract the exponents when dividing the powers with the same base.

22. Power of a power:
Ex:
NOTE:
keep the base and multiply the exponents.
Multiply the exponents, not add them!

23. Zero exponent law:
Ex:
Any power raised to an exponent of zero equals one.
NOTE:
No matter how big the number is, as long as it has zero as an exponent, it equals to one. Except

24. Negative exponents:
Ex:
To make an exponent positive, flip the base.
NOTE:
This does not change the sign of the base.

25. Ex:
Multiplying Polynomials:
In multiplying polynomials, you have to multiply the coefficients and add up the exponents of the variables with the same base.

26. Dividing polynomials:
Ex:
When dividing polynomials, you must divide the coefficients(if possible) and subtract the exponents of the variables with the same base.

27. Please simplify the following equations:
How?:
Answer:

28. Please simplify the following equations:
How?:
Answer:

29. Please simplify the following equations:
How?:
Answer:

30. Please simplify the following equations:
How?:
Answer:

31. Please simplify the following equations:
How?:
Answer:

32. Please simplify the following equations:
How?:
Answer:

33. Review

34. Copy and complete each of the following questions.

35. 1.) b2 * b7 1.) b9 2.) (p3)4 2.) p12 3.) (a2)3 * a3 3.) a9
4.) x2 * (xy)2
4.) x4y2
5.) (4m)2 * m3
5.) 16m5
6.) (3a)3*(2p)2
6.) 108a3p2

36. 7.)82*(xy)2*2x
7.) 128x3y2
8.) w3 * (3w)4
8.) 81w7
9.) q0
9.) 1
10.) p-2
10.) 1/p2
11.)(a2b)0
11.) 1
12.)(x-2y3)-2
12.) x4/y6

37. 13.) p p2
13.) p2
14.) 3b b5
14.) 1/3b3
15.) (4x2) x4
15.) 4

38. 16.) x2 * y0 * x3 * y-4
16.) 9y4/x

39. 17.) m 3 * m2n n
17.) m5/n7
18.) 3a b b * 32 * a
18.) 6a5/b4

40. 19) (3/4)3
19) 27/64
20) 2+3(4)2
20) 50