﻿ Unit 3 Section 1 : Index Notation

# Unit 3 Section 1 : Index Notation

Here we revise the use of index notation. You will already be familiar with the notation for squares and cubes

this is generalised by defining:

## Example 1

Calculate the value of:

 (a) 52 (b) 25 (c) 33 (d) 104

## Example 2

Fill in the missing number or numbers:

 (a) 2 = 2 × 2 × 2 × 2 × 2 × 2 × 2 (b) 9 = 3 (c) 1000 = 10 (d) 53 = × ×

## Example 3

 (a) Determine 25. (b) Determine 23. (c) Determine 25 ÷ 23. (d) Express your answer to (c) in index notation.

## Exercises

Question 1
Calculate:
 (a) 23 (b) 102 (c) 32 (d) 103 (e) 92 (f) 33 (g) 24 (h) 34 (i) 72
Question 2
Fill in the missing numbers:
 (a) 10 × 10 × 10 × 10 × 10 = 10 (b) 3 × 3 × 3 × 3 = 3 (c) 7 × 7 × 7 × 7 × 7 = 7 (d) 8 × 8 × 8 × 8 × 8 = 8 (e) 5 × 5 = 5 (f) 19 × 19 × 19 × 19 = 19 (g) 6 × 6 × 6 × 6 × 6 × 6 × 6 = 6 (h) 11 × 11 × 11 × 11 × 11 × 11 = 11
Question 3
Fill in the missing numbers:
 (a) 8 = 2 (b) 81 = 3 (c) 100 = 10 (d) 81 = 9 (e) 125 = 5 (f) 1 000 000 = 10 (g) 216 = 6 (h) 625 = 5
Question 4
Is 102 bigger than 210 ?
, because 102 = and 210 =
Question 5
Is 34 bigger than 43 ?
, because 34 = and 43 =
Question 6
Is 52 bigger than 25 ?
, because 52 = and 25 =
Question 7
Fill in the missing numbers:
 (a) 49 = 2 (b) 64 = 3 (c) 64 = 6 (d) 64 = 2 (e) 100 000 = 5 (f) 243 = 5
Question 8
Calculate:
 (a) 22 + 23 (b) 22 × 23 (c) 32 + 22 (d) 32 × 22 (e) 23 × 103 (f) 103 + 25
Question 9
Calculate:
 (a) (3 + 2) 4 (b) (3 – 2) 4 (c) (7 – 4) 3 (d) (7 + 4) 3
Question 10