# Chapter 1

Mind Map by closetkido, updated more than 1 year ago
 Created by closetkido over 4 years ago
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Indices + Surds

## Resource summary

Chapter 1
1 Surds
1.1 Simplifying
1.1.1 Find something that can be simplified
1.1.1.1 sqrt(16)=4
1.1.1.2 sqrt(25)=5
1.2 Rationalising
1.2.1 Simple
1.2.1.1 Multiply by the root on top and bottom
1.2.1.1.1 sqrt(7) x sqrt(7) = 7
1.2.2 Complex
1.2.2.1 Multiply by the same numbers with opposite add/subtract sign
1.2.2.1.1 3+sqrt(7) x 3-sqrt(7) = 9+7 = 16
2 Indices
2.1 Rules of Indices
2.1.1.1 Factors with different indices do not combine by addition or subtraction they stay separate.
2.1.2 Division
2.1.2.1 Subtract the indices
2.1.2.1.1 e.g. 2^5 / 2^3 = 2^2 as 5-3 = 2.
2.1.3 Multipication
2.1.3.1.1 e.g. 2^5 x 2^3 = 2^8 as 5+3 = 8
2.1.4 Brackets
2.1.4.1 Multiply the brackets
2.1.4.1.1 e.g. (2^5)^3 = 2^15 as 5 x 3 = 15
2.2 More Indices
2.2.1 Negative Powers
2.2.1.1 If power is negative, then flip and make power positive
2.2.1.1.1 e.g. 2x^-2 = 2/x^2
2.2.2 Fractional Powers
2.2.2.1 x^a/b = (brt(x))^a
2.2.2.1.1 e.g. x^4/3 = (4rt(x))^3
2.2.3 Equations
2.2.3.1 When moving fractional powers, flip but keep +- the same
2.2.3.1.1 e.g. x^2/3 = 100 ==> x = 100^3/2
2.2.3.2 Moving integer powers
2.2.3.2.1 If positive, then make a root.
2.2.3.2.1.1 e.g. x^3 = 100 => x = 3rt(100)
2.2.3.2.2 If negative, then make into fraction and cross-multiply.
2.2.3.3 Moving fractional powers
2.2.3.3.1 If positive, then make power.
2.2.3.3.1.1 e.g. x^1/2 = 100 => x = 100^2
2.2.3.3.2 If negative, the move over the other side, and flip top and bottom then simplify.
2.2.3.3.2.1 e.g. x^-3/2 = 100 => x = 100^-2/3

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