### Edexcel GCSE Maths

Numbers
Algebra
Geometry and Measures
Probability
Statistics

# The Laws of Indices

## Introduction to Indices

An index or power is a small number placed above and to the right of a base number. The index indicates how many times the base number should be multiplied by itself.

For example, can be written as . The base is , and the exponent is . It is read as “ to the power of .”

Let’s look at some more examples:

## Laws of Indices

### Multiplying indices

When multiplying indices with the same base, we add the powers:

Examples:

### Dividing indices

When dividing indices with the same base, we subtract the powers:

Examples:

### Power of a power

When raising an index to another power, we multiply the powers:

Examples:

### Power of a product

When raising a product to a power, we distribute the power to each factor:

Examples:

### Power of zero

Any non-zero number raised to the power of is equal to :

(where )

Examples:

### Negative indices

A negative index represents the reciprocal of the positive index:

Examples:

## Using the Laws of Indices to Simplify Numbers and Equations

We can use the laws of indices to simplify numbers and calculations. For example:

If , then

Let’s look at two more examples:

Simplify:

1.

2.

3.

4.

5.

6.

1.

2.

3.

4.

5.

6.

Simplify

Quizzes