L# 2 INDICES

1. Indices

An index number is a number which is appears in the power. The power, also known as the index, it tells us how many times we have to multiply the number by itself. For example, 2⁴ means that you have to multiply 2 by itself four times = 2×2×2×2 = 16.

 Important rules of indices

1)                               y^a × y^b = y^a+b

Examples

2⁵ × 2⁸ = 2¹³

5⁴ × 5^-3 = 5¹

2)                                 y^a ÷ y^b= y^a-b

Examples

3¹⁰ ÷ 3⁴ = 3⁶

7³ ÷ 7⁵ = 7^-2

3)                                  y ^-b = 1/y^b

Examples

2^-3 = 1/2³ = 1/8

4-1 = 1/4

4)                                y^m/n = (ⁿ√y)^m

Examples

25^1/2 = √25 = 5

8^2/3 = (³√8)² = 4

5)                                  (yⁿ)^m = y^nm

Example

2⁵ + 8⁴

= 2⁵ + (2³)⁴

= 2⁵ + 2¹²

6)                               y⁰ = 1

Example

5⁰ = 1

                                                           by:  Sir BAQAR