**What Are The Laws of Indices In Math? O Level Exam Preparation Guide**

This revision note aims to help your child revise the Laws of Indices and become proficient in solving the questions.

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**What Are Indices?**

Index numbers (indices) in Maths is the power or exponent which is raised to a number or a variable.

Power means the number of times a base number is multiplied by itself.

For example, in 2^{3}, 3 is the index of the power of 2.

2 to the power of 3 means

2^{3} = 2 × 2 × 2

If the index notation is a^{n}, *a* is known as base and *n* is the index or power.

a^{n} = a × a × a ….. × a (n times)

In order to do well for Secondary Math, you must be familiar with the Indices Law.

**What are the Laws of Indices?**

The laws of indices provide us with simple ways to handle expressions involving powers. Here, we introduce 6 indices laws: (1) Same Bases, (2) Same Index but Different Base, (3) Power Law, (4) Negative Indices, (5) Fraction Indices, and (6) Zero Indices.

**Same Base**

#### 1. Addition Law

If you multiply two variables with the same base, you need to add the powers and raise them to

that base.

Example: 2^{3} × 2^{6} = 2^{9}

#### 2. Subtraction Law

If you divide two variables with the same base, you need to subtract the powers and raise the new

power to the same base.

a^{m} ÷ a^{n} = a^{m−n}

Example: 2^{7} ÷ 2^{2} = 2^{5}

**Same index but different base**

#### 3. When you multiply two variables with different bases, but with the same indices,

you have to multiply its base and raise the same index to the multiplied variables.

a^{m} × b^{m} = (a × b)^{m}

Example: 2^{3} × 5^{3} = 10^{3}

#### 4. When you divide two variables with different bases, but with the same indices, you

need to divide the bases and raise the same index to the divided variables.

**Power Law**

#### 5. When a variable with some index is again raised with a different index, then you

need to multiply both indices together and raise it to the same base

(a^{m})^{n }= a^{mn}

Example: (2^{3})^{4 }= 2^{12}

**Negative Indices**

#### 6. If the index is a negative value, then it can be shown as the reciprocal of the

positive index raised to the same variable.

**Fraction Indices**

#### 7. An index in the form of a fraction can be represented as the radical form (with a

square root).

**Zero Indices**

#### 8. If the index number is ‘0’, then the result is ‘1’ regardless of the base.

a^{0} = 1

Example: 2^{0} = 1

After you are familiar with the Laws of Indices, lets explore some common Indices Math problems to help you understand how to apply them.

**Types of Indices Math Problems (With Solutions)**

**Indices Simplification Involving Multiplication and Division**

**Indices Simplification Involving Changing to Same Base**

**Indices Simplification Involving Negative and Fractional Index**

**Solving Indices Equation involving same base or same index**

**Solving Indices Equation by Substitution (For A-Math Students)**

**Solving Indices Simultaneous Equations (For A-Math Students)**

**Get Specialised Guidance on Indices**

Indices is a crucial chapter in Secondary Maths.

It also lays the foundations of more advanced topics like Differentiation and Integration in Additional Maths.

Make sure you understand the meaning of index form, the laws of indices and the different types of Indices Math problems.

If you need more help with this chapter, feel free to check our Secondary Math Tuition.

## Last Minute Revision for O Level Math?

## Check out our exam guide on other topics here!

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To Your Child’s Success,

Mr Tan Kok Heng

NIE Trained

Math Specialist

Jimmy Maths and Grade Solution Learning Centre

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