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- 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. 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. “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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. http://passyworldofmathematics.com Visit our site for Free Mathematics PowerPoints

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