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Radical Exponents (2)

In this worksheet, students multiply numbers with radical exponents.

'Radical Exponents (2)' worksheet

Key stage:  KS 4

Curriculum topic:  Number

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

Difficulty level:  

down

Worksheet Overview

QUESTION 1 of 10

A radical is a square root, a cube root, a fourth root, a fifth root etc...

 

The symbol   n   is used to represent the nth root.

5√32 = 2 because 25 = 32

4√81 = 3 because 34 = 81

 

 We can also write   4√81 as 81¼

because 81¼ x  81¼ x  81¼ x  81¼ =  811 = 81

 

This worksheet is about using the rule that

(ab)n = anbn

or its converse

anbn = (ab)n

 

and the rule that

 ap/q = (a1/q)p

 

Example

Work out, without a calculator,

8¾ x  32¾

 

Answer

This is

(8¼ x  32¼)3

or (4√8 x 4√32)3

 

Now...

8¼ 32¼  =  (8 x 32)¼ =  256¼

 

4√256 = 4 because 44 = 256

 

Now we must cube the result to get 43 = 64

Work out, without a calculator,

 

8¾ x   2¾

Work out, without a calculator,

 

1¾ x   1¾

Work out, without a calculator,

 

33/2 x   33/2

Work out, without a calculator,

 

33/2 x   123/2

Work out, without a calculator,

 

23/2 x   323/2

Work out, without a calculator,

 

25/2 x   85/2

Work out, without a calculator,

 

27¾ x   3¾

Work out, without a calculator,

 

92/3 x   32/3

Work out, without a calculator,

 

125¾ x   5¾

Work out, without a calculator,

 

122/3 x   182/3

  • Question 1

Work out, without a calculator,

 

8¾ x   2¾

CORRECT ANSWER
8
EDDIE SAYS
(8 × 2)¼
= 16¼
= 4√16
= 2
2³ = 8
  • Question 2

Work out, without a calculator,

 

1¾ x   1¾

CORRECT ANSWER
1
EDDIE SAYS
(1 × 1)¼
= 1¼
= 4√1
= 1
1sup3; = 1
  • Question 3

Work out, without a calculator,

 

33/2 x   33/2

CORRECT ANSWER
27
EDDIE SAYS
(3 × 3)½
= 9½
= √9
= 3
3³ = 27
  • Question 4

Work out, without a calculator,

 

33/2 x   123/2

CORRECT ANSWER
216
EDDIE SAYS
(3 × 12)½
= 36½
= √36
= 6
6³ = 216
  • Question 5

Work out, without a calculator,

 

23/2 x   323/2

CORRECT ANSWER
512
EDDIE SAYS
(2 × 32)½
= 64½
= √64
= 8
8³ = 512
  • Question 6

Work out, without a calculator,

 

25/2 x   85/2

CORRECT ANSWER
1024
EDDIE SAYS
(2 × 8)½
= 16½
= √16
= 4
45 = 1024
  • Question 7

Work out, without a calculator,

 

27¾ x   3¾

CORRECT ANSWER
27
EDDIE SAYS
(27 × 3)¼
= 81¼
= 4√81
= 3
3³ = 27
  • Question 8

Work out, without a calculator,

 

92/3 x   32/3

CORRECT ANSWER
9
EDDIE SAYS
(9 × 3)1/3
= 271/3
= 3√27
= 3
3² = 9
  • Question 9

Work out, without a calculator,

 

125¾ x   5¾

CORRECT ANSWER
125
EDDIE SAYS
(125 × 5)¼
= 625¼
= 4√625
= 5
5³ = 125
  • Question 10

Work out, without a calculator,

 

122/3 x   182/3

CORRECT ANSWER
36
EDDIE SAYS
(12 × 18)1/3
= 2161/3
= 3√216
= 6
6² = 36
---- OR ----

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