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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:
- ya × yb = ya+b
Examples
24 × 28 = 212
54 × 5-2 = 52
-
ya ÷ yb= ya-b
Examples
39 ÷ 34 = 35
72 ÷ 75 = 7-3
-
y -b = 1/yb
Examples
2-3 = 1/23 = 1/8
3-1 = 1/3
-
ym/n = (n√y)m
Examples
161/2 = √16 = 4
82/3 = (3√8)2 = 4
-
(yn)m = ynm
Example
25 + 84
= 25 + (23)4
= 25 + 212
-
y0 = 1
Example
50 = 1
