Exponents!

Definitions Superscript: Another name for an exponent (X 2, Y 2 ) Subscript: labels a variable (X 2, Y 2 ) Base: The number that is being multiplied (10 2 ) 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 (10 2 ) Power: a number identifying how many times to multiply a number (10 2 )

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

Standard and Extended Form in Base (10 1 ) + 4 (10 0 ) (10 1 ) + 5(10 0 ) (2 * 2) (5 * 5 * 5)

Standard and Extended Form in Base (10 2 ) + 6(10 1 ) + 3 (10 0 ) (10 3 ) + 2(10 2 ) + 6(10 1 ) + 0(10 0 ) (6 * 6 * 6 * 6) (8 * 8 * 8 * 8 * 8)

Adding Numbers With Exponents = (2 * 2) + (2 * 2) = (10 * 10 * 10) + (10 * 10 * 10) = (4 * 4) + (4 * 4) = (10 * 10) (10 * 10 * 10 * 10) = 2 8 _________________ (2 * 2 * 2) + (2 *2 *2 *2 *2)

Subtracting Numbers With Exponents = (4 * 4) - (2 * 2) 5 3 – 10 3 = -875 ________ (5 * 5 * 5) – (10 * 10 * 10) 5 2 – 3 2 = (5 * 5) – (3 * 3) 10 4 – 6 = (10 * 10 * 10 * 10) – (10 * 10 *10 * 10 * 10 * 10)

Multiplying Numbers With Exponents (10 2 ) * (10 2 ) = (10 * 10) (10 * 10) (2 4 ) * (2 6 ) = (2 * 2 * 2 * 2) (2 * 2 * 2 * 2 * 2 * 2) 4 (2 * 4) = (3 * 2) = 10 6

Dividing Numbers With Exponents (10 2 ) / (10 4 ) = (10 * 10) / (10 * 10 * 10 * 10) (2 6 ) / (2 4 ) = 2 2 (2 * 2 * 2 *2 *2 *2) / (2 * 2 *2 * 2) 10 (6/2) = (10/2) = 4 5

Exponents With Variables X * X = X 2 X * X * X = X 3 X * X * X * X = X 4 X * X * X * X * X = X 5 Y * Y = Y 2 Y * Y * Y = Y 3 Y * Y * Y * Y = Y 4 Y * Y * Y * Y * Y = Y 5

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 ,900,000  x  9.8 x  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 square r= rubas n= 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 4 th Plan The Advisors suggest a 4 th plan 1.20 rubas on the first square 2.25 on the second square 3.30 on the third square 4. Cover the entire 64 square board Should the peasant take this deal?

Exponential Growth/Decay Growth Equation y= a(1+b)^x y= final amount after a period of time a= the original amount b= the growth/decay factor (in a decimal) x= time

Exponential Growth/Decay Decay Equation y= a(1-b)^x y= final amount after a period of time a= the original amount b= the growth/decay factor (in a decimal) x= time

Stamp Investigation

Roots Opposite of a power PowerRoot Squared (^2)Square Root Cubed (^3)Cube Root

Roots Use a calculator to find roots. 1.Find the square root of Find the square root of Find the square root of Find the cube root of Find the cube root of 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 Base Base Base Base 4

Using Other Bases 2418 Base 9 2(9 3 ) + 4(9 2 ) + 1(9 1 ) + 8(9 0 ) = 2(729) + 4(81) + 1(9) + 8(1) = = = Base 6 5(6 4 ) + 2(6 3 ) + 3(6 2 ) + 1(6 1 ) + 0(6 0 ) = 5(1296) + 2(216) + 3(36) + 1(6) + 0(1) = = = 7026

Using Other Bases Base 2 1(2 5 ) + 0(2 4 ) + 1(2 3 ) + 0(2 2 ) + 1(2 1 ) + 0(2 0 ) = = = Base (4 4 ) + 1(4 3 ) + 3(4 2 ) + 1(4 1 ) + 2(4 0 ) = 2(256) + 1(64) + 3(16) + 1(4) + 2(1) = = = 630