**Summary**

MUST Remember all these Rules of Indices:

1.

2.

3.

4.

5.

6.

7.

8.

### 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:

**Rule #1:**

When we **multiply** two numbers which have the **same base**, we **add** their powers.

**Rule #2:**

When we **divide** two number which have the **same base**, we **subtract** their powers.

**Rule #3:**

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.

#### Examples

**Q.** Solve:

*Solution:*

We know Rule #1 will apply here, hence for:

**Ans:**

**Q.**

*Solution:*

Apply Rule #1:

**Ans:**

**Q.**

*Solution:*

**Ans:**

**Q.**

*Solution:*

Apply Rule #2:

**Ans:**

**Q.**

*Solution:*

Apply Rule #2:

**Ans:**

**Q.**

*Solution:*

Apply Rule #3:

**Ans:**

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.

**Rule #4:**

When we **multiply** two numbers which have** different base** but **same powers**, we then **multiply** the base numbers but the **power remains the same**.

**Rule #5:**

When we **divide** two numbers which have **different base** but **same powers**, we then **divide** the** base** numbers but the **power remains the same**.

**Rule #6:**

When power of any constant or variable is 0 then that constant or variable is equal to 1.

**Rule #7:**

A negative power means the constant or variable is on the bottom line of the fraction.

**Rule #8:**

Roots can be written as powers as well.

#### Examples

**Q.** Solve:

*Solution:*

Let:

**equation 1**

Then:

As is not possible, we take

Put *y* in equation 1:

This shows that:

**Ans:**

#### Reference

- CGP AS Level Mathematics Edexcel