 # Recognise Powers of 2, 3, 4 and 5

In this worksheet, students will calculate powers up to 5 (2, 3, 4 and 5) and roots, building up recognition of the most common examples and their products. Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   Pearson Edexcel, OCR, Eduqas, AQA

Curriculum topic:   Number, Indices and Surds

Curriculum subtopic:   Structure and Calculation, Powers and Roots

Difficulty level:   ### QUESTION 1 of 10

What is a power?

Powers are where we multiply numbers by themselves a given number of times.

They can also be called indices and orders.

ab

The bottom number (called the base) is the number we are multiplying together.

The top number (the power, index or order) is how many of them we will multiply together.

e.g. 23 means to multiply three numbers 2s together (2 x 2 x 2).

You will be expected to know the powers for 2, 3, 4 and 5:

Powers of 2

 21 22 23 24 25 2 2 x 2 2 x 2 x 2 2 x 2 x 2 x 2 2 x 2 x 2 x 2 x 2 2 4 8 16 32

Powers of 3

 31 32 33 34 35 3 9 27 81 243

Powers of 4

 41 42 43 44 45 4 16 64 256 1024

Powers of 5

 51 52 53 54 55 5 25 125 625 3125

In this activity, we will calculate powers up to 5 and roots, building up recognition of the most common examples and their products.

Complete the sentence below to provide the alternative descriptions of powers.

Evaluate:

32

Match each number written as a power to its true value.

## Column B

24
27
33
8
23
16
52
64
43
25

Match each number to the series of powers it can also represent.

## Column B

27
Power of 4
125
Not a power of 2, 3, 4 or 5
1024
Power of 3
8
Power of 5
48
Power of 2

Evaluate the powers of 3 below.

 Value 32 34 35

Evaluate the powers of 5 below.

 Value 52 53 55

Which is larger?

32 or 23

32

23

Which is larger?

54 or 45

54

45

Order these numbers from smallest to largest:

43, 52, 34

In the boxes, type '1' for the first number in the list, '2' for the second, etc.

 Order 43 52 34

Order these numbers in descending order:

43, 52 , 34

In the boxes, type '1' for the first number in the list, '2' for the second, etc.

 Order 43 52 34
• Question 1

Complete the sentence below to provide the alternative descriptions of powers.

EDDIE SAYS
The top numbers in a power can also be called indices or orders. All three of these mean the same thing so, if you ever see any of these words, you will be doing the same calculations. Where have you seen the word 'indices' or 'orders' before? That's right, in our BODMAS or BIDMAS process - its the second stage!
• Question 2

Evaluate:

32

9
EDDIE SAYS
32 means that you multiply two number 3s together: 3 x 3 = 9 Don't let the word 'evaluate' throw you here - it is just an alternative way of saying 'calculate' or 'work out'.
• Question 3

Match each number written as a power to its true value.

## Column B

24
16
33
27
23
8
52
25
43
64
EDDIE SAYS
All you need to remember here is that the bottom number is the number you are multiplying with and the top number (the index) is how many times you multiply it. e.g. 45 = 4 x 4 x 4 x 4 x 4 = 1024 24 = 2 x 2 x 2 x 2 = 16 33 = 3 x 3 x 3 = 27 23 = 2 x 2 x 2 = 8 52 = 5 x 5 = 25 43 = 4 x 4 x 4 = 63
• Question 4

Match each number to the series of powers it can also represent.

## Column B

27
Power of 3
125
Power of 5
1024
Power of 4
8
Power of 2
48
Not a power of 2, 3, 4 or 5
EDDIE SAYS
This question is testing if you can remember the information from the Introduction. The first five powers of 5 are: 5, 25, 125, 625, 3125 All of these numbers are, therefore, powers of 5. Flip back to the Introduction here if you mismatched any. Try to commit as many of these as you can to memory.
• Question 5

Evaluate the powers of 3 below.

 Value 32 34 35
EDDIE SAYS
Remember that the power tells us how many of the base number to multiply together. So 33 is the same as multiplying 3 number 3s together. 32 = 3 x 3 = 9 34 = 3 x 3 x 3 x 3 = 81 35 = 3 x 3 x 3 x 3 x 3 = 243
• Question 6

Evaluate the powers of 5 below.

 Value 52 53 55
EDDIE SAYS
This is the same as the last question, we have just changed our base number. Remember that the power tells us how many of the base number to multiply together. 54 is the same as multiplying 4 number 5s together. 52 = 5 x 5 = 25 53 = 5 x 5 x 5 = 125 55 = 5 x 5 x 5 x 5 x 5 = 3125
• Question 7

Which is larger?

32 or 23

32
EDDIE SAYS
To decide which is larger, we need to work them out: 23 = 2 x 2 x 2 = 8 32 = 3 x 3 = 9 Which number out of 8 and 9 is larger then?
• Question 8

Which is larger?

54 or 45

45
EDDIE SAYS
To decide which is larger, we need to work them out: 54 = 5 x 5 x 5 x 5 = 625 45 = 4 x 4 x 4 x 4 x 4 = 1024 Which of these two numbers is larger?
• Question 9

Order these numbers from smallest to largest:

43, 52, 34

In the boxes, type '1' for the first number in the list, '2' for the second, etc.

 Order 43 52 34
EDDIE SAYS
Just work these out and put them in order! 43 = 64 52 = 25 34 = 81 If we order these, we should have: 25, 64, 81 Did you type the correct number next to each option to show this order?
• Question 10

Order these numbers in descending order:

43, 52 , 34

In the boxes, type '1' for the first number in the list, '2' for the second, etc.

 Order 43 52 34
EDDIE SAYS
Did you think we'd given the same question twice?! We were testing if you were reading the question carefully. Descending order means largest to smallest. Let's work these out: 43 = 4 x 4 x 4 = 64 52 = 5 x 5 = 25 34 = 3 x 3 x 3 x 3 = 81 So in descending order, these would be: 81, 64, 25 Great job, that's another activity complete!
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