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1. 1
2 =2=2
2
2 =2x2= 4
3
2 =2x2x2= 8
4
2 = 2 x 2 x 2 x 2 = 16
5
2 = 2 x 2 x 2 x 2 x 2 = 32
6
2 = 2 x 2 x 2 x 2 x 2 x 2 = 64
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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 multiplications
of 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 them
34 means three multiplied by itself four times:
34 = 3 x 3 x 3 x 3 = 9 x 9 = 81
four of them
25 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
2
1 = 1x1 = 1
22 = 2x2 = 4
2
3 = 3x3 = 9 3
42 = 4x4 = 16
52 = 5x5 = 25
2
6 = 6x6 = 36 Area = 3 x 3 = 9
72 = 7x7 = 49

7. Powers of Three are called “CUBES”,
because they form the volume of cubes.
3
13 = 1 x 1 x 1 = 1
23 = 2 x 2 x 2 = 8
3 3
3 = 3 x 3 x 3 = 27
43 = 4 x 4 x 4 = 64
53 = 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 the
values 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 that
tells 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 2
from Power
22 = 2 x 2 = 4
Subtract 1
from Power Divide by 2
21 = 2 = 2
Subtract 1
Divide by 2
from Power 20 = 1
Any Number to the Power of Zero Equals 1 : a0 = 1

12. Write the “Expanded Form”, and then Multiply out
the 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 big
Base the number of times the little index digit tells
us 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 done
the 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

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