# 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.