All About Index Notation

Index Notation or exponents The numbers 1, 2, 4, 8, 16, 32, 64, 128, 256, ... form a pattern. What is the rule for this pattern? Exponential Form

Factor Form

Standard Form

2 0 = Any number (except 0) raised to the zero power is always equal to 1.

1

2 1 = Any number raised to the first power is always equal to itself.

2

22 = 2 x 2 =

4

23 = 2 x 2 x 2 =

8

24 = 2 x 2 x 2 x 2 =

16

25 = 2 x 2 x 2 x 2 x 2 =

32

26 = 2 x 2 x 2 x 2 x 2 x 2 =

64

27 = 2 x 2 x 2 x 2 x 2 x 2 x 2 =

128

28 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 =

256

Can you predict the next two numbers in the list after 256?

Authored by Fathima Nacchiar

Index Notation or exponents Example 1:

Rewrite the numbers 1, 3, 9, 27, 81, 243, ... as a powers of 3.

Solution: Exponential Form

Standard Form

30 =

1

31 =

3

32 =

9

33 =

27

34 =

81

35 =

243

Can you predict the next two numbers in the list after 243?

Authored by Fathima Nacchiar

Index Notation or exponents Exercises Write each of the following in index form 2x2x2 9x9x9 5x5x5 12 x 12 = 4x4x4

x2x2x2= x9= x5x5x5x5x5x5x5x5= x4x4x4x4=

Write each of the following in full 43 76 9³ 3² 87 If 7 3 = 343, then find 7 4 with only one multiplication. If 4 5 = 1,024, then find 4 6 with only one multiplication The numbers 1, 6, 36, 216, 1296, ... are each powers of what number?

Authored by Fathima Nacchiar