# Dividing Indices

In this worksheet, students divide numbers expressed using indices.

Key stage:  KS 3

Curriculum topic:  Number

Curriculum subtopic:  Understand Integer Powers/Real Roots

Difficulty level:

### QUESTION 1 of 10

An index is sometimes called a power or an exponent.

In 54, the 4 is the index and the 5 is the base.

54 is read as "5 to the power 4" or "5 to the 4" and means 5 x 5 x 5 x 5.

Dividing numbers

When we divide numbers with the same base number, we can just subtract the indices.

57 ÷ 53 = 54

This is because, when we divide we can cancel a 5 on the top with a 5 on the bottom, leaving four 5s on the top.

Simplify:

57 ÷ 55

52

252

12

Simplify:

48 ÷ 44

42

12

44

Simplify:

35 ÷ 34

39

31.25

3

Simplify:

34 ÷ 32

32

36

38

Simplify:

55 ÷ 53

52

258

58

Simplify:

35 ÷ 31

96

34

35

Simplify:

55 ÷ 55

51

0

1

Simplify:

34 ÷ 34

344

31

30

Simplify:

408 ÷ 404

2

402

404

Simplify:

64 ÷ 60

64

640

60

• Question 1

Simplify:

57 ÷ 55

52
• Question 2

Simplify:

48 ÷ 44

44
• Question 3

Simplify:

35 ÷ 34

3
• Question 4

Simplify:

34 ÷ 32

32
• Question 5

Simplify:

55 ÷ 53

52
• Question 6

Simplify:

35 ÷ 31

34
• Question 7

Simplify:

55 ÷ 55

1
• Question 8

Simplify:

34 ÷ 34

30
EDDIE SAYS
This shows that 30 = 1
• Question 9

Simplify:

408 ÷ 404

404
• Question 10

Simplify:

64 ÷ 60

64
EDDIE SAYS
This suggests that 60 = 1
---- OR ----

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