EDEXCEL GCSE FOUNDATION MATHS - What are Indices

EDEXCEL GCSE Foundation Maths - What are Indices?

What are Indices?

Indices (also known as exponents) are a shorthand way of representing repeated multiplication.

The Basics

• Base: The number being multiplied.
• Index (or Exponent): The number of times the base is multiplied by itself.

Example: * 2^3 means 2 multiplied by itself 3 times: 2 x 2 x 2 = 8

Types of Indices

• Square: An index of 2. Example: 3^2 = 3 x 3 = 9
• Cube: An index of 3. Example: 2^3 = 2 x 2 x 2 = 8
• Other Indices: Indices can be any whole number. Example: 5^4 = 5 x 5 x 5 x 5 = 625

Important Rules

• Anything to the power of 1 is itself: 5^1 = 5
• Anything to the power of 0 is 1: 7^0 = 1
• Negative indices: a^-n = 1/a^n (a cannot be 0)
• Fractional indices: a^(1/n) = n?a (where n is a positive integer)

Examples

• Calculate 4^3:
• 4^3 = 4 x 4 x 4 = 64
• Simplify 2^-2:
• 2^-2 = 1/2^2 = 1/4
• Calculate 8^(1/3):
• 8^(1/3) = ?8 = 2

Key Points

• Indices are a fundamental concept in mathematics.
• Understanding them is crucial for further study in algebra, geometry, and calculus.
• Practice is key to mastering indices!

Try These!

1. Calculate 3^4.
2. Simplify 5^-1.
3. Calculate 16^(1/2).

Answers

1. 81
2. 1/5
3. 4

Next Steps

• Explore the rules of indices in more detail.
• Learn about operations involving indices (addition, subtraction, multiplication, division).
• Practice solving problems involving indices.