EDEXCEL GCSE FOUNDATION MATHS - What are Negative Indices

Edexcel GCSE Foundation Maths - What are Negative Indices?

Understanding the Basics

You've probably encountered positive indices like 2², which means 2 multiplied by itself twice (2 x 2 = 4). Negative indices work similarly, but they represent a reciprocal.

Reciprocal

The reciprocal of a number is 1 divided by that number. For example:

• Reciprocal of 2 is 1/2
• Reciprocal of 5 is 1/5
• Reciprocal of 10 is 1/10

Negative Indices and Reciprocals

A number raised to a negative index is the same as its reciprocal raised to the positive value of that index.

Example:

• 3?² is the same as (1/3)²

Calculating Negative Indices

1. Find the reciprocal of the base number.
2. Raise the reciprocal to the positive value of the index.

Example:

Calculate 4?³

1. Reciprocal of 4 is 1/4
2. (1/4)³ = (1/4) x (1/4) x (1/4) = 1/64

Therefore, 4?³ = 1/64

Important Note:

• Any number raised to the power of -1 is its reciprocal. For example, 5?¹ = 1/5
• A number raised to the power of 0 is always 1. For example, 5? = 1

Example Questions

1. Calculate 2??
2. What is the reciprocal of 7?²?
3. Simplify 5?¹ x 5³

Answers:

1. 2?? = (1/2)? = 1/16
2. 7?² = 1/7² = 1/49, so the reciprocal is 49/1
3. 5?¹ x 5³ = (1/5) x (5 x 5 x 5) = 5² = 25

Practice Makes Perfect

Practicing these calculations will help you understand negative indices better. Work through the examples and try the practice questions. You can also find more examples and exercises in your textbook or online.