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Mixed Indices

In this worksheet, students understand and use fractional and negative indices.

'Mixed Indices' worksheet

Key stage:  KS 4

Curriculum topic:  Number

Curriculum subtopic:  Calculate with Roots and Integer (Fractional) Indice

Difficulty level:  

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Worksheet Overview

QUESTION 1 of 10

A fractional index of a half is the equivalent of finding a square root.

 

Using the rules for multiplying powers, notice that:

9½ x 9½ = 91

 

This must be the equivalent of:

√9 x √9 = 9

 

so

9½ = √9 = 3

 

A negative index means "1 over". 

 

So:

 

And:

 

 

Select the answer which is equal to:

 

5-1

-5


0.2

Select the answer which is equal to:

 

64½

8

64½

16

Select the answer which is equal to:

 

2-1

1

½

-21

Select the answer which is equal to:

 

4

-2

½

-4.5

Select the answer which is equal to:

 

25

0.2

-√12.5

√25

Select the answer which is equal to:

 

81½

40.5

9

81½

Select the answer which is equal to:

 

4-2

1

-8

1/16

Select the answer which is equal to:

 

10000

1000

0.01

10½

Select the answer which is equal to:

 

1000

33.3

100

1/√1000

Select the answer which is equal to:

 

12100½

1100

√121

110

  • Question 1

Select the answer which is equal to:

 

5-1

CORRECT ANSWER
0.2
  • Question 2

Select the answer which is equal to:

 

64½

CORRECT ANSWER
8
  • Question 3

Select the answer which is equal to:

 

2-1

CORRECT ANSWER
½
  • Question 4

Select the answer which is equal to:

 

4

CORRECT ANSWER
½
  • Question 5

Select the answer which is equal to:

 

25

CORRECT ANSWER
0.2
  • Question 6

Select the answer which is equal to:

 

81½

CORRECT ANSWER
9
  • Question 7

Select the answer which is equal to:

 

4-2

CORRECT ANSWER
1/16
  • Question 8

Select the answer which is equal to:

 

10000

CORRECT ANSWER
0.01
  • Question 9

Select the answer which is equal to:

 

1000

CORRECT ANSWER
1/√1000
  • Question 10

Select the answer which is equal to:

 

12100½

CORRECT ANSWER
110
---- OR ----

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