Index notation: first steps

The Maths Habit

How could you write this list in a shorter way?

Shoppingmilkmilkmilkmilkmilkmilkbread

6 milk, 1 bread. Count the ones that are the same. Maths has a short way too.

24
Base
The number that is multiplied.
24
Index
The small raised number. It counts how many of the base are multiplied.
2×2×2×2→24
Index form
A short way to write the same number multiplied again and again.

Is it the same number multiplied each time?

A3 × 3 × 3Yes
B4 × 2 × 4No: not the same number
C6 × 6Yes
D5 + 5 + 5No: adding

Write 2 × 2 × 2 × 2 in index form.

1Count them.
2×12×22×324
How many 2s?4
2Write the index form.
Index form24

Write 6 × 6 × 6 in index form.

1Count them.
6×16×263
How many 6s?3
2Write the index form.
Index form63

Write 2 × 2 × 2 × 2 in index form.

1Count them.
2×12×22×324
How many 2s?4
2Write the index form.
Index form24
1Count them.2Write the index form.

Write 7 × 7 × 7 × 7 in index form.

1Count them.
7×17×27×374
How many 7s?4
2Write the index form.
Index form74

Write 2 × 2 × 2 × 2 in index form.

1Count them.
2×12×22×324
How many 2s?4
2Write the index form.
Index form24
1Count them.2Write the index form.

Write 3 × 3 in index form.

1Count them.
3×132
How many 3s?2
2Write the index form.
Index form32

Write 2 × 2 × 2 × 2 in index form.

1Count them.
2×12×22×324
How many 2s?4
2Write the index form.
Index form24
1Count them.2Write the index form.

Write 8 × 8 × 8 × 8 × 8 in index form.

1Count them.
8×18×28×38×485
How many 8s?5
2Write the index form.
Index form85

Index notation: first steps worksheet, page 1

Work out.

4 × 28
8 × 216
9 × 327

23 means 2 × 2 × 2.

2×2×2

It never means 2 × 3.

Work out 24.

1Write it out.
2×2×2×2
2Multiply one at a time.
2×2=4
4×2=8
8×2=16
24 =16

Work out 33.

1Write it out.
3×3×3
2Multiply one at a time.
3×3=9
9×3=27
33 =27

Work out 24.

1Write it out.
2×2×2×2
2Multiply one at a time.
2×2=4
4×2=8
8×2=16
24 =16
1Write it out.2Multiply one at a time.

Work out 52.

1Write it out.
5×5
2Multiply one at a time.
5×5=25
52 =25

Work out 24.

1Write it out.
2×2×2×2
2Multiply one at a time.
2×2=4
4×2=8
8×2=16
24 =16
1Write it out.2Multiply one at a time.

Work out 103.

1Write it out.
10×10×10
2Multiply one at a time.
10×10=100
100×10=1000
103 =1000

Work out 24.

1Write it out.
2×2×2×2
2Multiply one at a time.
2×2=4
4×2=8
8×2=16
24 =16
1Write it out.2Multiply one at a time.

Work out 23.

1Write it out.
2×2×2
2Multiply one at a time.
2×2=4
4×2=8
23 =8

Index notation: first steps worksheet, page 2

Answer sheet

Is it right?
Thumbs up: right. Thumbs down: wrong.

  1. 23 = 6

    Wrong: 2 × 2 × 2 = 8

  2. 32 = 9

    Right: 3 × 3 = 9

  3. 4 × 4 × 4 = 43

    Right: three 4s

  4. 5 × 5 × 5 × 5 = 53

    Wrong: four 5s, 54

  5. 102 = 20

    Wrong: 10 × 10 = 100

  1. Which is bigger, 25 or 52?

    25 = 32, bigger than 52 = 25

  2. Write 1000 in index form with a base of 10.

    103

  3. Write 16 in index form in two different ways.

    42 and 24

  1. Write 4 × 4 × 4 in index form.

    43
    4×14×2431Countthem.How many 4s?2Write theindex form.Index form

  2. Work out 23.

    8
    ××1Write itout.2Multiply oneat a time.×=×=23 =

  3. Write 5 × 5 in index form. Then work it out.

    52 = 25
Exit tickets to print