Indices

An index number is a number which is raised to a power. The power, also known as the index, tells you how many times you have to multiply the number by itself. For example, 2⁵ means that you have to multiply 2 by itself five times = 2 × 2 × 2 × 2 × 2 = 32.

There are a number of important rules of index numbers:

• y^a × y^b = y^a+b

Examples

2⁴ × 2⁸ = 2¹²

5⁴ × 5^-2 = 5²

• y^a ÷ y^b = y^a-b

Examples

3⁹ ÷ 3⁴ = 3⁵

7² ÷ 7⁵ = 7^-3

• y ^-b =  1
             y^b

Examples

2^-3 = 1/2³ = 1/8

3^-1 = 1/3

• y^m/n = (ⁿÖy)^m

Examples

16^1/2 = Ö16 = 4

8^2/3 = (³Ö8)² = 4

• (yⁿ)^m = y^nm

Example

2⁵ + 8⁴

= 2⁵ + (2³)⁴

= 2⁵ + 2¹²

• y⁰ = 1

Example

5⁰ = 1