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12 =2=2 22 =2x2= 4 32 =2x2x2= 8 42 = 2 x 2 x 2 x 2 = 16 52 = 2 x 2 x 2 x 2 x 2 = 32 62 = 2 x 2 x 2 x 2 x 2 x 2 = 64       ...
What do you notice about the numbers:       2, 4, 8, 16, 32, 64- They are all computer memory and storage  numbers, like 1...
“Exponents”, “Indices”, “Powers”, and “Indexes” are all descriptions of the exact same thing.They are all a shorthand way ...
53 means five multiplied by itself three times:53 = 5 x 5 x 5 = 25 x 5 = 125     three of them34 means three multiplied by...
The little number “2” is called the                          “Index” or “Power” and tells us                          how ...
Powers of Two are called “SQUARES”,because they form the area of squares.                            3 21    =   1x1   = 1...
Powers of Three are called “CUBES”,because they form the volume of cubes.                            313 = 1 x 1 x 1 = 123...
2         5 = 5 x 5 = 25 5   2         is called “Index Form”5 x 5 is called “Expanded Form” 25       is called “Numerical...
Write the “Index Form” and then Multiply out thevalues to get the “Numerical Form” answer.   1) 4 x 4 = _____ = _____   2)...
The “Base” is the number we are multiplying.The “Index” or “Power” is the little number thattells us how many multiplies w...
The Index Power of Zero works out like this:Subtract 1             23 = 2 x 2 x 2 = 8                                     ...
Write the “Expanded Form”, and then Multiply outthe values to get the “Numerical Form” answer.   1) 34 = _________________...
To get “Expanded Form”, we Multiply out the bigBase the number of times the little index digit tellsus to. We can then wor...
Algebra Exponents with letters as bases are donethe exact same way as number exponents.   1) m4 = m x m x m x m   2) k0 = ...
It is important never to get the following mixed up   Multiplication involves a group of Additions              3n = n + n...
http://passyworldofmathematics.com   Visit our site for Free Mathematics PowerPoints
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Basic Exponents and Indices

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Basic Exponents and Indices

  1. 1. 12 =2=2 22 =2x2= 4 32 =2x2x2= 8 42 = 2 x 2 x 2 x 2 = 16 52 = 2 x 2 x 2 x 2 x 2 = 32 62 = 2 x 2 x 2 x 2 x 2 x 2 = 64 Image Source: http://www.mydigitallife.info
  2. 2. What do you notice about the numbers: 2, 4, 8, 16, 32, 64- They are all computer memory and storage numbers, like 16 Gig, 32 Gig, 64 Gig on an iPad. Power of 2 exponents are the basis of all computing which is done in “Binary” or base 2 numbers like these.
  3. 3. “Exponents”, “Indices”, “Powers”, and “Indexes” are all descriptions of the exact same thing.They are all a shorthand way of writing multiplicationsof the same item several times.32 means three multiplied by itself two times:32 = 3 x 3 = 9 ( The 3 is multiplied out twice).32 does not mean 3 x 2 = 6 ( 3 x 2 means 2 lots of 3, or 3 + 3, and does not = 3 x 3 )
  4. 4. 53 means five multiplied by itself three times:53 = 5 x 5 x 5 = 25 x 5 = 125 three of them34 means three multiplied by itself four times:34 = 3 x 3 x 3 x 3 = 9 x 9 = 81 four of them25 means two multiplied by itself five times:25 = 2 x 2 x 2 x 2 x 2 = 8 x 4 = 32 five of them
  5. 5. The little number “2” is called the “Index” or “Power” and tells us how many times to multiply out the big number “5”The big number “5” is called the “base”and is what we multiply together 2 5 = 5 x 5 = 25 Multiply two of them
  6. 6. Powers of Two are called “SQUARES”,because they form the area of squares. 3 21 = 1x1 = 122 = 2x2 = 4 23 = 3x3 = 9 342 = 4x4 = 1652 = 5x5 = 25 26 = 6x6 = 36 Area = 3 x 3 = 972 = 7x7 = 49
  7. 7. Powers of Three are called “CUBES”,because they form the volume of cubes. 313 = 1 x 1 x 1 = 123 = 2 x 2 x 2 = 8 3 33 = 3 x 3 x 3 = 2743 = 4 x 4 x 4 = 6453 = 5 x 5 x 5 = 125 3 Volume = 3 x 3 x 3 = 27
  8. 8. 2 5 = 5 x 5 = 25 5 2 is called “Index Form”5 x 5 is called “Expanded Form” 25 is called “Numerical Form”
  9. 9. Write the “Index Form” and then Multiply out thevalues to get the “Numerical Form” answer. 1) 4 x 4 = _____ = _____ 2) 3 x 3 x 3 = _____ = _____ 3) 2 x 2 x 2 x 2 x 2 = _____ = _____ 4) 5 = ____ = _____
  10. 10. The “Base” is the number we are multiplying.The “Index” or “Power” is the little number thattells us how many multiplies we are doing. 1) 4 x 4 = 42 = 16 2) 3 x 3 x 3 = 33 = 27 3) 2 x 2 x 2 x 2 x 2 = 25 = 32 4) 5 = 51 = 5 Any Number to Power of 1 = the Number
  11. 11. The Index Power of Zero works out like this:Subtract 1 23 = 2 x 2 x 2 = 8 Divide by 2from Power 22 = 2 x 2 = 4Subtract 1from Power Divide by 2 21 = 2 = 2Subtract 1 Divide by 2from Power 20 = 1 Any Number to the Power of Zero Equals 1 : a0 = 1
  12. 12. Write the “Expanded Form”, and then Multiply outthe values to get the “Numerical Form” answer. 1) 34 = ___________________ = ____ 2) 80 = special rule = ___ 3) 24 = ____________________ = ____ 4) 7831 = just one 783 = _______
  13. 13. To get “Expanded Form”, we Multiply out the bigBase the number of times the little index digit tellsus to. We can then work out the number answer. 1) 34 = 3 x 3 x 3 x 3 = 81 2) 80 = “special rule” = 1 3) 24 = 2 x 2 x 2 x 2 = 16 4) 7831 = just one 783 = 783
  14. 14. Algebra Exponents with letters as bases are donethe exact same way as number exponents. 1) m4 = m x m x m x m 2) k0 = “special rule” = 1 3) (bh)2 = bh x bh = b x b x h x h = b2 h2 4) y1 = just one y = y
  15. 15. It is important never to get the following mixed up Multiplication involves a group of Additions 3n = n + n + n Powers involve a group of Multiplications 3 n =nxnxn
  16. 16. http://passyworldofmathematics.com Visit our site for Free Mathematics PowerPoints

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