## Overview

This covers; Laws of Indices, Fractional and Negative Powers, Standard Form (building on knowledge gained in Complex Calculations and Accuracy) and Surds. Some of this is quite complicated (some Grade A and A* questions). I think the trick is to make sure you understand the basics thoroughly before moving on to the more advanced stuff.

## Indices and Standard Form Questions

- Work out the value of;

a) (3³ x 5² x 10) x (3–2 x 5–1 x 10²)

a) (10–2)–2

b) 9² x 3√27 ÷ 4√320

a) 811/4

b) 62525

- Write the following using index notation:

a) (4√13)4

b) (4√11)2

a) 216−2÷3

b) 81−3÷4

a) (3.2 x 10–5) x (8 x 10–3)

b) (3 x 10–7) ÷ (8 x 10–1)

c) (1.6 x 104) + (2.4 x 105)

d) (6.07 x 105) — (1.8 x 103)

(√32 — 2)(√72 + 1)

## Indices and Standard Form Approach

- These look scary but you can just break them down in a few steps. Let’s look at question 1a):-

See final answer to parts a) and b) below

b) In this question you need to divide the indices using rule:- x√Wy = W(y/x)

- Again, use the rule — x√Wy = W(y/x)

Remember that the question asks for answers in index notation i.e xy

Remember to give answers in standard form i.e. Y x 10n (with Y a number between 1 and 10 and n is an integer).

## Indices and Standard Form Answers

- a)

54 x 33 = 625 x 27 =16,875

b) 64 x 10³ = 1,296,000

b) 9² x 3√27 ÷ 4√320

= 81 x 3 x 35 = 59,049

b) 62525 = 4√625= 5

- a) (4√13)4 = 131 = 13

b) (4√11)2 = 112/4 = 115

= 1/3√2162 = 1/62 = 1/36

- b) 81−3÷4 = 1/813/4

= 1/4√813 = 1/33 = 1/27

b) (3 x 10–7) ÷ (8 x 10–1) = 3/8 x 10–7/10–1

=0.375 x 10–6 = 3.75 x 10–7

c) (1.6 x 104) + (2.4 x 105) = 16,000 + 240,000 = 256,000 = 2.56 x 105

d) (6.07 x 105) — (1.8 x 103) = 607,000 — 1,800 = 605,200 =6.052 x 105

(When multiplying out the first part of this sum note that: 2√8 x 3√8 = 2 x √8 x √8 x 3 = 6 x 8 = 48)

Therefore (2√8 — 2)(3√8 + 1) = 48 + 2√8 — 6√8 — 2 =

46 — 4√8