Exponents!

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)

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)

Standard and Extended Form in Base 10

1. 34 ----------------------------------- 3(101) + 4 (100)

2. 45------------------------------------ 4(101) + 5(100)

3. 22------------------------------------------------------- (2 * 2)

4. 53------------------------------------------------------ (5 * 5 * 5)

Standard and Extended Form in Base 10

1. 563 ---------------------- 5(102) + 6(101) + 3 (100)

2. 1260------------1(103) + 2(102) + 6(101) + 0(100)

3. 64------------------------------------------------------- (6 * 6 * 6 * 6)

4. 85---------------------------------------------------- (8 * 8 * 8 * 8 * 8)

Adding Numbers With Exponents

22 + 22 = 8 ---------------------- (2 * 2) + (2 * 2)

103 + 103 = 2000 -------(10 * 10 * 10) + (10 * 10 * 10)

42 + 42 = 32 ------------------ (4 * 4) + (4 * 4)

10 2 + 4 = 106 -------------- (10 * 10) (10 * 10 * 10 * 10)

2 3 + 5 = 28 _________________ (2 * 2 * 2) + (2 *2 *2 *2 *2)

Subtracting Numbers With Exponents

42 - 22 = 12 ---------------- (4 * 4) - (2 * 2)

53 – 103 = -875 ________ (5 * 5 * 5) – (10 * 10 * 10)

52 – 32 = 16 -------------- (5 * 5) – (3 * 3)

104 – 6 = 10-2 --------------------------(10 * 10 * 10 * 10) – (10 * 10 *10 * 10 * 10 * 10)

Multiplying Numbers With Exponents

(102) * (102) = 104 ---------------- (10 * 10) (10 * 10)

(24) * (26) = 210 --------------------------(2 * 2 * 2 * 2) (2 * 2 * 2 * 2 * 2 * 2)

4(2 * 4) = 48

10 (3 * 2) = 106

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

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

FOIL Review

1. (X + 3)(X + 4) =

2. (X + 5)(X + 6) =

3. (X – 4)(X – 3) =

4. (X – 2)(X – 2) =

Scientific Notation• Used when a number is too large for a calculator• Move the decimal place until you only have a

digit 1 thru 9 and a decimal number

• 12,000,000,000 1.2 x 1010

• 678,900,000 6.789 x 108

• 0.000000000098 9.8 x 10-11

• 0.007897 7.897 X 10-3

Checkers Investigation

See Growing, Growing, Growing pg. 7

Checkers Investigation Extension

Plan 2: A new 16-square board, 1 ruba on the first square, 3 on the second square

Plan 3: The queen is not happy with the king. She suggests a 12-square board, 1 ruba on the first square, use the equation r = 4^ n-1 to figure out how many rubas will be on each squarer= rubasn= the square number

Comparing the Plans

1. Make a table for all 3 plans up to square 10

2. Make a graph with all 3 plans on it (Use 3 different colors)

3. How many rubas are on the final square for each plan?

4. Which plan is best for the peasant? Which plan is best for the king?

A 4th Plan

The Advisors suggest a 4th plan

1. 20 rubas on the first square2. 25 on the second square3. 30 on the third square4. Cover the entire 64 square board

Should the peasant take this deal?

Exponential Growth/Decay

GrowthEquation y= a(1+b)^x

y= final amount after a period of timea= the original amountb= the growth/decay factor (in a decimal)x= time

Exponential Growth/Decay

DecayEquation y= a(1-b)^x

y= final amount after a period of timea= the original amountb= the growth/decay factor (in a decimal)x= time

Stamp Investigation

Roots

Opposite of a power

Power Root

Squared (^2) Square Root

Cubed (^3) Cube Root

Roots

Use a calculator to find roots.

1. Find the square root of 64.2. Find the square root of 100.3. Find the square root of 36.4. Find the cube root of 64.5. Find the cube root of 27.6. Find the cube root of 8.

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)

Using Other Bases

• 2418 Base9

• 52310 Base6

• 101010 Base2

• 21312 Base4

Using Other Bases

• 2418 Base9

2(93) + 4(92) + 1(91) + 8(90) = 2(729) + 4(81) + 1(9) + 8(1) =1458 + 324 + 9 + 8 == 1799• 52310 Base6

5(64) + 2(63) + 3(62) + 1(61) + 0(60) =

5(1296) + 2(216) + 3(36) + 1(6) + 0(1) =6480 + 432 + 108 + 6 + 0 == 7026

Using Other Bases

• 101010 Base2

1(25) + 0(24) + 1(23) + 0(22) + 1(21) + 0(20) =160 + 0 + 8 + 0 + 2 + 0 ==170• 21312 Base4

• 21312• 2(44) + 1(43) + 3(42) + 1(41) + 2(40) =• 2(256) + 1(64) + 3(16) + 1(4) + 2(1) =• 512 + 64 + 48 + 4 + 2 =• = 630