Unit 2 Section 3 : Index Notation

In the previous section on prime factors, you will have seen occasional use of index notation.
For example, the number 360 can be written as either 2×2×2×3×3×5 or as 23 × 32 × 5.

23 is pronounced "2 to the power of 3" or "2 cubed", and means 2 × 2 × 2.
32 is pronounced "3 to the power of 2" or "3 squared", and means 3 × 3.

In general, an is pronounced "a to the power of n" and means "n lots of a, multiplied together".

                  

Numbers written in index notation are often called powers.
Strictly speaking, a is the base number, and n is the power.

Using a calculator

A calculator can be used to work out one number to the power of another.
The index button is usually marked xy or yx.

Sometimes you need to press SHIFT or 2ndF to use this button
For example, to calculate 54, you may need to press

You should find out which buttons you need to use on your calculator.
Make sure that you get the correct answer of 625 for the calculation above.

Practice Questions

Work out the answers to the questions below then click on the button marked Click on this button below to see the correct answer to see whether you are correct.

Practice Question 1

(a) Calculate 24

(b) Calculate 73

(c) Calculate 105

Practice Question 2

(a) What is the missing number in the statement below?

(b) What is the missing number in the statement below?

 

Exercises

Work out the answers to the questions below and fill in the boxes. Click on the Click this button to see if you are correct button to find out whether you have answered correctly. If you are right then will appear and you should move on to the next question. If appears then your answer is wrong. Click on to clear your original answer and have another go. If you can't work out the right answer then click on Click on this button to see the correct answer to see the answer.

Question 1
Fill in the missing powers in the following statements:
(a) 6 × 6 × 6 × 6 × 6 = 6
(b) 3 × 3 × 3 × 3 = 3
(c) 7 × 7 × 7 × 7 × 7 × 7 = 7
(d) 9 × 9 × 9 = 9
Question 2
Calculate:
(a) 23 =
(b) 33 =
(c) 104 =
(d) 53 =
(e) 27 =
(f) 34 =
(g) 92 =
(h) 103 =
(i) 107 =
Question 3
Fill in the missing bases and powers in the statements below:
(a)
100 = 10
(b)
81 = 2
(c)
81 = 4
(d)
16 = 4
(e)
16 = 2
(f)
7 = 2401
Question 4
Calculate:
(a) 52 × 22 =
(b) 32 × 24 =
(c) 72 × 23 =
(d) 62 × 2 =
(e) 92 × 3 =
(f) 53 × 23 =
Question 5
Fill in the missing powers in each of the statements below:
(a)
23 × 25 = (2×2×2) × (2×2×2×2×2)
= 2×2×2×2×2×2×2×2
=
2
(b)
57 × 52 = (5×5×5×5×5×5×5) × (5×5)
= 5×5×5×5×5×5×5×5×5
=
5
(c)
64 × 62 = 6
(d)
73 × 72 = 7
(e)
86 × 8 = 8
Question 6
Fill in the missing powers in the statements below:
(a)
93 = 9×9×9
= (3×3)×(3×3)×(3×3)
= 3×3×3×3×3×3
=
3
(b)
94 = 9×9×9×9
= (3×3)×(3×3)×(3×3)×(3×3)
= 3×3×3×3×3×3×3×3
=
3
Question 7
Use a similar method to the one shown in Question 6 to fill in the powers in the following statements:
(a)
42 = 2
(b)
212 = 4
(c)
1254 = 5
Question 8
Fill in the missing numbers in the following statements:
(a)
54 × 24 = 10
(b)
35 × 25 = 6
(c)
4 × 23 = 83
(d)
75 × 35 = 21
(e)
74 × 4 = 284
(f)
59 × 9 = 109

You have now completed Unit 2 Section 3
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