1. Exponents!

2. Definitions
Superscript: Another name for an exponent (X2, Y2) Subscript: labels a variable (X2 , Y2) Base: The number that is being multiplied (102) Exponent: a symbol that is written above and to the right of a number to show how many times the number is to be multiplied by itself (102) Power: a number identifying how many times to multiply a number (102)

3. Definitions Continued
Squared: When a number is raised to the second power (22) Cubed: When a number is raised to the third power (23) Standard Form: A number that is condensed into its simplest form (23 , 22 ) Extended Form: A number written out in multiples (2 * 2 * 2) , (2 * 2 * 2 * 2)

4. Standard and Extended Form in Base 10
(101) + 4 (100)
(101) + 5(100)
(2 * 2)
(5 * 5 * 5)

5. Standard and Extended Form in Base 10
(102) + 6(101) + 3 (100)
(103) + 2(102) + 6(101) + 0(100)
(6 * 6 * 6 * 6)
(8 * 8 * 8 * 8 * 8)

6. Adding Numbers With Exponents
= (2 * 2) + (2 * 2) = (10 * 10 * 10) + (10 * 10 * 10) = (4 * 4) + (4 * 4) = (10 * 10) (10 * 10 * 10 * 10) = 28 _________________ (2 * 2 * 2) + (2 *2 *2 *2 *2)

7. Subtracting Numbers With Exponents
= (4 * 4) - (2 * 2) 53 – 103 = -875 ________ (5 * 5 * 5) – (10 * 10 * 10) 52 – 32 = (5 * 5) – (3 * 3) 104 – 6 = (10 * 10 * 10 * 10) – (10 * 10 *10 * 10 * 10 * 10)

8. Multiplying Numbers With Exponents
(102) * (102) = (10 * 10) (10 * 10) (24) * (26) = (2 * 2 * 2 * 2) (2 * 2 * 2 * 2 * 2 * 2) 4(2 * 4) = (3 * 2) = 106

9. Dividing Numbers With Exponents
(102) / (104) = 10-2 (10 * 10) / (10 * 10 * 10 * 10) (26) / (24) = 22 (2 * 2 * 2 *2 *2 *2) / (2 * 2 *2 * 2) 10(6/2) = 103 4(10/2) = 45

10. Exponents With Variables
X * X = X2
X * X * X = X3
X * X * X * X = X4
X * X * X * X * X = X5
Y * Y = Y2
Y * Y * Y = Y3
Y * Y * Y * Y = Y4
Y * Y * Y * Y * Y = Y5

11. FOIL Review (X + 3)(X + 4) = (X + 5)(X + 6) = (X – 4)(X – 3) =

12. Checkers Investigation

13. Using Other Bases
Base 2 (0, 1) Base 3 (0, 1, 2) Base 4 (0, 1, 2, 3) Base 5 (0, 1, 2, 3, 4) Base 6 (0, 1, 2, 3, 4, 5) Base 7 (0, 1, 2, 3, 4, 5, 6) Base 8 (0, 1, 2, 3, 4, 5, 6, 7) Base 9 (0, 1, 2, 3, 4, 5, 6, 7, 8) Base 10 (0, 1, 2, 3, 4, 5, 6, 7, 8, 9)

14. Using Other Bases
2418 Base9
52310 Base6
Base2
21312 Base4

15. Using Other Bases 2418 Base9 2(93) + 4(92) + 1(91) + 8(90) =
 2(93) + 4(92) + 1(91) + 8(90) =
2(729) + 4(81) + 1(9) + 8(1) = =
= 1799
52310 Base6
  5(64) + 2(63) + 3(62) + 1(61) + 0(60) =
5(1296) + 2(216) + 3(36) + 1(6) + 0(1) = =
= 7026

16. Using Other Bases
Base2
1(25) + 0(24) + 1(23) + 0(22) + 1(21) + 0(20) = =
=170
21312 Base4
21312
2(44) + 1(43) + 3(42) + 1(41) + 2(40) =
2(256) + 1(64) + 3(16) + 1(4) + 2(1) = =
= 630