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
Writing your answers in index form, calculate:
(a) 102 × 103
(b) 23 × 27
(c) 34 ÷ 32
(d) 25 ÷ 22
(e) 106 ÷ 102
(f) 54 ÷ 52
Question 11

(a) Without using a calculator, write down the values of k and m.

64 = 82 = 4k = 2m
k =
m =

(b) Complete the following:

215 = 32 768
214 =