1. Index notation
Mathematicians have a special shorthand way of writing some multiplication calculations.
The small numbers are called index numbers or powers
5x5 can be written as We say 5 to the power of 2
5x5x5 can be written as We say 5 to the power of 3

2. Checking answers

3. Squared and Cubed
Sometimes to the power 2 is called squared, and to the power 3 is called cubed.
So, 4 squared is 42 = 4x4 and has a value of 16 ( because 4x4 = 16) and
4 cubed is 43 = 4x4x4 and has a value of 64 (because 4x4x4 = 64)

4. Q3 Checking Answers (a) 6 squared is 62 = 6x6 and has a value of ……
(b) 10 squared is …..2 = …x…. and has a value of ……
(c) 2 cubed is 23 = ….x….x…..and has a value of 8
(d) 5 cubed is ….3 = ….x….x…. and has a value of …..

5. Powers of 10 Example 102 = 10 x 10 = 100 in words (One Hundred)
Checking your Answers
(a) 103 = 10 x 10x 10 = ……. in words (One ……………..)
(b) 10? = 10 x 10 x 10 x10 = in words (…………………………)
(c) …… = 10 x 10 x 10 x 10 x 10 x 10 = ………………. in words ( one ………...)
(d) 105 = ……………………………… = in words (One Hundred ………...)

6. You can see from your previous work that
Working Backwards
Example
What number do your square and get 16 ?
You can see from your previous work that
42 = 16. So the answer is 4.
To save on writing mathematicians use a symbol to stand for “what do you square to get” it looks like this √ or √ and is called the square root.
So √16 is “ the square root of 16” and has a value of 4

7. Checking Answers

8. Cube roots The symbol 3√ is used for the cube root of a
number. For example,
3√8 is the cube root of 8 and has a value of 2
(because 2x2x2 = 8)

9. Using a calculator Most scientific calculators will have a square
root button and cube root button.
For most modern calculators you key in the
sequence in the order you think about it.
For example, to find the value of √6
you would press √ then 6 then =
And see

10. Calculations with numbers in index form
53 is a short way of writing 5x5x5.
The calculation 53 x 52 = 5x5x5 x 5x5 = 55
1 If you look closely there is a quick way of finding the answer.
34 x 35 = 3?
What number should (?) become ?
2 Explain why.

11. Division As division is the opposite of multiplication,
what do you think the (?) should become in the
example below. ?
38 ÷ 33 = 3?