Exponents!.

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Presentation transcript:

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 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 10 563 ---------------------- 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 (X + 3)(X + 4) = (X + 5)(X + 6) = (X – 4)(X – 3) =

Checkers Investigation

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(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