EXPONENTS AND RADICALS WORKSHEET WITH ANSWERS

Question 1 :

Write the following in the form of 5ⁿ :

(i) 625

(ii)  1/5

(iii)  √5

(iv)  √125

Question 2 :

Write the following in the form of 4ⁿ :

(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) (³√49)⁵

(iv) (1/³√100)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  =  5^1/2

(iv)  √125

Solution :

√125  =  (5^1/2)³

=  5^3/2

Question 2 :

Write the following in the form of 4ⁿ :

(i) 16

Solution :

16  =  4 x 4  =  4²

(ii)  8  

Solution :

8  =  2 x 4

  =  √4 x 4

  =  4^3/2

(iii)  32  

Solution :

32  =  2 x 4 x 4

  =  √4 x 4²

  =  4^5/2

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  =  5^1/2

(ii)  √7

Solution :

√7  =  7^1/2

(iii) (³√49)⁵

Solution :

(³√49)⁵  =  (49^1/3)5

 =  (7²)^5/3

 =  7^10/3

(iv) (1/³√100)⁷

Solution :

(1/³√100)⁷  =  (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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