## LEARNING OBJECTIVES:

- To define index and base of a number
- To discuss the different laws of indices
- To evaluate expressions using the laws of indices

## MATH CONCEPTS

**INDEX OF A NUMBER-**The index of a number tells how many times to use the number in a multiplication. It is written as a small number to the right and above the base number. It is also known as exponent or power.**BASE OF A NUMBER-**It is the number that gets multiplied when using an index or exponent.**THE THREE BASIC LAWS OF INDICES**For any real number x, y, m, and n, the following rules uphold:**Multiplication Law****/ Product Rule****Division Law/Quotient Rule****Power Law/Power Rule**

**Other Laws:**

**IMPORTANCE**

- Understanding the laws of indices plays an important role in manipulating and simplifying expressions involving indices.
- Laws of indices can also be used to evaluate expressions involving indices without the use of calculators.

## DISCUSSION

**BASE AND INDEX OF A NUMBER**

It is vital to get familiarized with the base and index of a number. This will become the foundation of learning the laws of indices. In the given example, 3 is raised to 5. Meaning, the base will be multiplied to itself five times.

If we will evaluate the given, 3 x 3 x 3 x 3 x 3 = 243.

## DISCUSSION

**LAWS OF INDICES **

**Multiplication Law/ Product Rule****–**When expressions with the same base (x) are multiplied, the indices (m and n) are added.

** **** ****Examples: **

1) 2) 3)

**Division Law/ Quotient Rule****–**When expressions with the same base (x) are divided, the indices (m and n) are subtracted.

** **** ****Examples: **

1) 2) 3)

**Power Law/ Power Rule****–**When an expression is raised to a certain index and is raised again to another index, the indices (m and n) are multiplied.

** **** ****Examples: **

1) 2) 3)

**ILLUSTRATIVE EXAMPLES **

Find the value of the following series.

**REFERENCES: **

- https://www.mathsisfun.com/definitions/index-power-.html
- https://www.mathsisfun.com/definitions/base-numbers-.html
- https://mathsmadeeasy.co.uk/gcse-maths-revision/rules-indices-gcse-maths-revision-worksheets/
- http://www.mathcentre.ac.uk/resources/Engineering%20maths%20first%20aid%20kit/latexsource%20and%20diagrams/2_1.pdf
- http://www.a-levelmathstutor.com/alg-indices.php
- https://revisionmaths.com/advanced-level-maths-revision/pure-maths/algebra/indices