Year 9 Maths Chapter 6 - Indices and surds
Table of Contents
Index notation
3 x 3 x 3 x 3 x 3 x 3 x 3 = 3⁷
Scientific notation
science!
a x 10ᵐ
where m is an integer
and 1 <= a < 10
Prime factorisation
Writing a number as a product of its prime factors.
108 = 2 x 2 x 3 x 3 x 3
= 2² x 3³
On Casio calculators, you can obtain the prime factorisation of any inputted number by pressing SHIFT + DMS button.
On Sharp calculators, well, I don’t know.
Index laws
Multiplication and division
aᵐ x bⁿ = aᵐ⁺ⁿ
aᵐ ÷ bⁿ = aᵐ⁻ⁿ
Powers and brackets
(aᵐ)ⁿ = aᵐⁿ
(ab)ᵐ = aᵐbᵐ
Powers and fractions
See Fractional indices for fractional indices.
(a/b)ᵐ = aᵐ/bᵐ
Zero index
a⁰ = 1
where a != 0
Negative indices
a⁻ᵐ = 1/aᵐ
Fractional indices
a¹/ᵐ = ᵐ√a
aˣ/ᵐ = ᵐ√aˣ
Surds
Surds are irrational numbers written with a radical sign. They cannot be expressed as a fraction.
For example, 5√6 is a surd. It means 5 x √6.
_
5√6
Surds
Addition and subtraction
You can only add or subtract surds if they are like surds. For example, 5√6, 3√6 and √6 are like surds. If you were to add or subtract these together:
5√6 + 3√6 + √6 = 9√6
5√6 - 3√6 - √6 = 5√6
Multiplication and division
a√b x c√d = ab√cd
√a / a \
–– = √| ––– |
√b \ b /
What a beautiful attempt at making a big bracket. I’m not bothered to go to the bracket making website right now so you’re going to have to deal with it.