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:

Example 2

Fill in the missing number or numbers:

Example 3

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 ?

- Yes No , because 10² = and 2¹⁰ =

Question 5
Is 3⁴ bigger than 4³ ?

- Yes No , because 3⁴ = and 4³ =

Question 6
Is 5² bigger than 2⁵ ?

- Yes No , 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 = 4^k = 2^m
k =
m =

(b) Complete the following:

2¹⁵ = 32 768
2¹⁴ =