# EXPONENTS AND RADICALS WORKSHEET WITH ANSWERS

Question 1 :

Write the following in the form of 5:

(i) 625

(ii)  1/5

(iii)  5

(iv)  √125

Question 2 :

Write the following in the form of 4:

(i) 16

(ii)  8

(iii)  32

Question 3 :

Find the value of

(i) (49) 1/2

(ii)  (243)2/5

(iii)  9-3/2

(iv)  (64/125)-2/3

Question 4 :

Use a fractional index to write:

(i)  √5

(ii)  √7

(iii) (349)5

(iv) (1/3100)7

Question 5  :

Find the 5th root of

(i) 32

(ii)  243

(iii)  100000

(iv)  1024/3125

## Detailed Answer Key

Question 1 :

Write the following in the form of 5n:

(i) 625

Solution :

625  =  5 x 5 x 5 x 5

=  54

(ii)  1/5

Solution :

1/5  =  5-1

(iii)  5

Solution :

√5  =  51/2

(iv)  √125

Solution :

√125  =  (51/2)3

=  53/2

Question 2 :

Write the following in the form of 4:

(i) 16

Solution :

16  =  4 x 4  =  42

(ii)  8

Solution :

8  =  2 x 4

=  √4 x 4

=  43/2

(iii)  32

Solution :

32  =  2 x 4 x 4

=  √4 x 42

=  45/2

Question 3 :

Find the value of

(i) (49) 1/2

Solution :

(49) 1/2  =  (72)1/2

=  7

(ii)  (243)2/5

Solution :

(243)2/5  =  (35)2/5

=  32

=  9

(iii)  9-3/2

Solution :

9-3/2  =  (32)-3/2

=  3-3

=  1/33

=  1/27

(iv)  (64/125)-2/3

Solution :

(64/125)-2/3  =  (125/64)2/3

=  [(5/4)3]2/3

=  (5/4)2

=  25/16

Question 4 :

Use a fractional index to write:

(i)  √5

Solution :

√5  =  51/2

(ii)  √7

Solution :

√7  =  71/2

(iii) (349)5

Solution :

(349) =  (491/3)5

=  (72)5/3

=  710/3

(iv) (1/3100)7

Solution :

(1/3100)=  (100-1/3)7

=  (10-2/3)7

=  10-14/3

Question 5  :

Find the 5th root of

(i) 32

5th root of 32  =  2

(ii)  243

5th root of 243 is 3.

(iii)  100000

5th root of 100000 is 10.

(iv)  1024/3125

5th root of 100000 is 4/5.

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