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Multiplying and Dividing Indices

In this worksheet, students practise multiplying and dividing indices.

'Multiplying and Dividing Indices' worksheet

Key stage:  KS 3

Curriculum topic:   Number

Curriculum subtopic:   Understand Integer Powers/Real Roots

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

This worksheet is about multiplying and dividing indices.

 

Example a4 × a2
= (a × a × a × a)   ×   (a × a)
= a4+2 = a6

 

To multiply terms containing the same letter in index form, add the powers.
 

Example 2 y7 × y3

= y7-3 = y4
 

 

To divide terms containing the same letter in index form, subtract the powers.

 

Work out:

 

a3 × a4 =
 
 

 

 

a7

a12

Work out:

 

a4 × a6 =
 
 

 

a46

a10

Work out:

 

a7 × a2 =
 
 

 

a9

2a9

Work out:

 

a6 × a7 =
 
 

 

a13

a10

Work out:

 

a6 ÷ a5 =
 
 

 

a

a11

Work out:

 

a9 ÷ a6 =
 
 

 

 

 

a3

a15

Work out:

y27 ÷ y3=
 
 

 

y24

y9

Work out:

 

y70 × y7=
 
 

 

Because we are multiplying these indices, we add the indices

y70 x y7 = y70+7  = y77

y490

y77

Work out:

 

y6 × y6 =
 
 

 

y36

y12

Work out:

 

y6 ÷ y6 =
 
 

 

1

y1

  • Question 1

Work out:

 

a3 × a4 =
 
 

 

 

CORRECT ANSWER
a7
EDDIE SAYS

Because we are multiplying these indices, we add the indices

a3 x a4 = a3+4  = a7

  • Question 2

Work out:

 

a4 × a6 =
 
 

 

CORRECT ANSWER
a10
EDDIE SAYS

Because we are multiplying these indices, we add the indices

a4 x a6 = a4+6  = a10

  • Question 3

Work out:

 

a7 × a2 =
 
 

 

CORRECT ANSWER
a9
EDDIE SAYS

Because we are multiplying these indices, we add the indices

a7 x a2 = a7+2  = a9

  • Question 4

Work out:

 

a6 × a7 =
 
 

 

CORRECT ANSWER
a13
EDDIE SAYS

Because we are multiplying these indices, we add the indices

a6 x a7 = a6+7  = a13

  • Question 5

Work out:

 

a6 ÷ a5 =
 
 

 

CORRECT ANSWER
a
EDDIE SAYS

Because we are dividing these indices, we subtract the indices

a6 ÷ a5 = a6-5  = a1

Remember that a1 should just be written as a

  • Question 6

Work out:

 

a9 ÷ a6 =
 
 

 

 

 

CORRECT ANSWER
a3
EDDIE SAYS

Because we are dividing these indices, we subtract the indices

a9 ÷ a6 = a9 - 6  = a3

 

  • Question 7

Work out:

y27 ÷ y3=
 
 

 

CORRECT ANSWER
y24
EDDIE SAYS

Because we are dividing these indices, we subtract the indices

y27 ÷ y3 = a27 - 3  = a9

 

  • Question 8

Work out:

 

y70 × y7=
 
 

 

Because we are multiplying these indices, we add the indices

y70 x y7 = y70+7  = y77

CORRECT ANSWER
y77
EDDIE SAYS

Because we are multiplying these indices, we add the indices

y70 x y7 = a70+7  = a77

  • Question 9

Work out:

 

y6 × y6 =
 
 

 

CORRECT ANSWER
y12
EDDIE SAYS

Because we are multiplying these indices, we add the indices

y6 ÷ y6 = y6+6  = y12

  • Question 10

Work out:

 

y6 ÷ y6 =
 
 

 

CORRECT ANSWER
1
EDDIE SAYS

Because we are dividing these indices, we subtract the indices

a6 ÷ a6 = a6-6  = a0

Remember that a0 should just be written as 1

---- OR ----

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