If a number is multipled together several times e.g. 3 × 3 × 3 × 3 × 3 if can be written in exponent form, 34

In the number 34, the 3 is called the base and the 4 is called the exponent, index orpower.

All mean the same thing!

Examples

32
9
33
27
34
81

Prime Factors

Natural numbers can be written as the product of prime numbers. These are best written in index form.

e.g. 36 = 2 × 2 × 3 × 3 = 22 × 32
12 = 2 × 2 × 3 = 22 × 3

Factor trees are useful for finding prime factors.

Y8_Exponents_01.gif

Square Roots

Squaring a number means multiplying it by itself.e.g. 32 = 3 × 3 = 9

Finding the square root of a number is the opposite or inverse of doing this.e.g. Y8_Exponents_03.gif

i.e. A number must be found which multiplies with itself to give the original number,

Some common square roots

1
4
9
16
25
36
49
64
81
100
121
144
400
10 000
1 000 000
1
2
3
4
5
6
7
8
9
10
11
12
20
100
1000

To find the square roots of numbers between the ones shown above, the easiest way is to use a calculator.

e.g. Y8_Exponents_02.gif (rounded to 3 decimal places).