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# What are Powers and Roots?

Maths | 11-13 yrs | Interactive

## What is the power of a number

When a number is multiplied by itself either once or several times, the number of times the number is multiplied is known as the power of a number.

Example –
a) Multiplied by itself
5 x 5

b) Multiplied by itself multiple times
3 x 3 x 3

We can also write these numbers in a different way.
5 x 5 = 52
Or
3 x 3 x 3 = 33
Or
6 x 6 x 6 x 6= 64

## What is an exponent, base and power in a number?

• The small number at the top is the exponent. It is how many times the number is multiplied by itself.
• The large number is called the base. It is the number that is being multiplied by it self.
• The power of the number is how many times the number is being multiplied by it self.

### How is the power of a number calculated?

The power of the number : 64 is
6 x 6 x 6 x 6 = 1296

The power of the number 72 is
7 x 7 = 49

## What is the root of a number?

The root of a number A is another number, which when multiplied by itself a given number of times, equals A.
a) 5 x 5= 25
The number 5 is the root of twenty five.

b) 6 x 6= 36.
The number 6 is the root of the number 36.

### How to calculate the root of a number?

Find the root of the number 16 :

Method –
16 is a small number – so it will be easy to figure out by multiplying small numbers by themselves:

1 x 1 = 1
2 x 2 = 4
3 x 3 = 9
4 x 4 = 16

So the root of the number 16 is 4.