Page 2: Indices - Powers and Roots
This page delves into the concept of indices, which is crucial for understanding how to estimate in maths and perform complex calculations efficiently.
The guide begins by explaining the basics of square numbers and cubes, providing examples such as 2² = 2 × 2 = 4 and 2³ = 2 × 2 × 2 = 8. It then progresses to higher powers, demonstrating how to calculate 2⁴ and 2⁵.
Definition: An index (plural: indices) is the power to which a number is raised.
The page introduces negative indices, explaining that they represent the reciprocal of the positive power. For instance, 2⁻² = 1/2².
Example: 2⁻³ = 1/2³ = 1/8
Fractional indices are also covered, with a focus on square roots and cube roots. The guide explains that a½ is equivalent to √a, and a⅓ is the cube root of a.
Highlight: Any number raised to the power of 0 equals 1, and any number raised to the power of 1 equals itself.
The page concludes with rules for multiplying and dividing indices with the same base, which are essential for estimating calculations in Maths Genie and similar resources.
Example: When multiplying indices with the same base, add the powers: 2³ × 2⁴ = 2³⁺⁴ = 2⁷
