Indices

[Hassab]

Powers and Roots

A power tells you to multiply a number by itself.

For example, 5^3 means 5 x 5 x 5 which is 125.

2^4 means 2 x 2 x 2 x 2 which is 16.

It is a short way of writing out calculations.

For example, 3^3 x 4^2 = 3 x 3 x 3 x 4 x 4 = 432

A root is the opposite of a power.



- means 'what number do you square to get 4?'


The answer is 2.


- means 'what number do you cube (multiply by itself 3 times) to get 27?'

The answer is 3.


Rules of indices

There are several rules that you will need to know.

Rule 1

When you multiply indices of the same number you add the powers.

For example: 5^4 x 5^3 = 5^4 + 3 = 5^7

Rule 2

When you divide indices of the same number you subtract the powers.


Rule 3

Indices outside a bracket multiply.

For example: (3^2) ^4 = 3^2 x 4 = 3^8

Rule 4

Negative indices mean reciprocal, i.e. 'one over...' or 'put on the bottom of a fraction'.


Rule 5

When the power is a fraction the top of the fraction (numerator) is a power and the bottom of the fraction is a root.


Rule 6

Anything to a power of 1 is just itself and we normally don't bother putting the 1 there i.e. 5^1 is just 5.

Anything to a power of 0 is equal to 1, it doesn't matter what number it is!

i.e. 10^0 = 1, 2^0 = 1, x^0 = 1, etc.

There you go! There's your rules. Now practice using them by doing some questions!


The rules of Indices also work in Algebra (after all the letters or variables represent numbers anyway!).

So with algebraic fractions you can take the powers at the bottom from the powers at the top and simplify the expression (a bit like cancelling the powers on the top and bottom of the fraction).[/size]