MUST Remember all these Rules of Indices:
What are Indices?
Just like other operations in maths (+, -, x,), Indices are a type of math operations. However they don’t have a fix symbol for it.
We can identify it from the way a certain number is written e.g where n is called an exponent/index/power and a is called the base. They tell us to take a number and multiply it by itself a certain no. of times which is called repeated multiplication.
It is defined as:
- When n is a positive integer, is defined as:
Some basic rules of Indices that you must remember are:
When we multiply two numbers which have the same base, we add their powers.
When we divide two number which have the same base, we subtract their powers.
When we have a power to the power of something else, we multiply the powers together.
To be able to understand these rules better, let’s go through some examples.
We know Rule #1 will apply here, hence for:
Apply Rule #1:
Apply Rule #2:
Apply Rule #2:
Apply Rule #3:
Furthermore, there are some more important rules which we should be familiar. We should understand how and when they are applied as all these rules are used a lot of times when integrating, differentiating and in other places.
When we multiply two numbers which have different base but same powers, we then multiply the base numbers but the power remains the same.
When we divide two numbers which have different base but same powers, we then divide the base numbers but the power remains the same.
When power of any constant or variable is 0 then that constant or variable is equal to 1.
A negative power means the constant or variable is on the bottom line of the fraction.
Roots can be written as powers as well.
As is not possible, we take
Put y in equation 1:
This shows that:
- CGP AS Level Mathematics Edexcel