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We know that 43 = 4 4 4 = 64. The 3 above the 4 tells us to multiply three 4s.

 

Similarly, 52 = 5 5 = 25. The 2 tells us to multiply two 5s.

 

This short-hand way of writing a number that is multiplied several times is called index notation. The special terms associated with index notation are demonstrated below.

 

Example 1
What is the base and the index of the number 64?

 

Base = 6

Index = 4

 

 

Example 2

Write 10 10 10 10 10 in index notation

 

10 10 10 10 10 = 105          (we are multiplying five 10s.)

 

 

Example 3

Write 36 in expanded form.

 

36 = 3 3 3 3 3 3     (six 3s)

 

 

Example 4

Write 5 5 5 5 3 3 3 in index notation.

 

5 5 5 5 3 3 3 = 54 33

 

In the Pop Quiz questions, 3^6 means 36. "^" means "to the power of".


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Question 1/5

1. 5 x 5 x 5 x 5 x 5 x 5 in index form is

15 625

6 ^ 5

30

5 ^ 6

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