5.2.1 Indices, PT3 Practice 1


5.2.1 Indices, PT3 Practice 1
Question 1:
  (a) Simplify: a4 ÷ a7
  (b)   Evaluate: ( 2 4 ) 1 2 × 3 1 2 × 12 1 2  

Solution:
  (a) a4 ÷ a7 = a4-7 = a-3

(b)
( 2 4 ) 1 2 × 3 1 2 × 12 1 2 = 2 2 × 3 1 2 × ( 4 × 3 ) 1 2 = 2 2 × 3 1 2 × ( 2 2 × 3 ) 1 2 = 2 2 × 3 1 2 × 2 × 3 1 2 = 2 3 × 3 = 24


Question 2:
  (a) Simplify: p3 ÷ p-5
  (b) Evaluate: 10 1 2 × 5 1 2 × ( 2 1 2 ) 5  

Solution:
  (a) p3 ÷ p-5 = p3-(-5) = p3+5 = p8

(b)
10 1 2 × 5 1 2 × ( 2 1 2 ) 5 = ( 2 × 5 ) 1 2 × 5 1 2 × 2 5 2 = 2 1 2 × 5 1 2 × 5 1 2 × 2 5 2 = 2 1 2 + 5 2 × 5 1 2 1 2 = 2 3 + 5 0 = 8 + 1 = 9


Question 3:
  (a) Find the value of 10 4 3 ÷ 10 1 3 .  
  (b)   Simplify (xy3)5 × x4.

Solution:
(a)
10 4 3 ÷ 10 1 3 = 10 4 3 1 3 = 10 3 3 = 10
  
  (b) ( x y 3 ) 5 × x 4 = x 5 y 15 × x 4 = x 5 + 4 y 15 = x 9 y 15


Question 4:
  (a) ( 81 a 8 ) 1 4 =    
  (b)   Find the value of 23 × 22

Solution:
(a)
( 81 a 8 ) 1 4 = 1 ( 81 a 8 ) 1 4 = 1 ( 3 4 ) 1 4 ( a 8 ) 1 4 = 1 3 a 2  

(b)
23 × 22 = 23+2 = 25 = 32


Question 5:
Find the value of the following.
  (a) 81 3 4 × 27 1    
  (b) 8 2 3 × 3 2  

Solution:
(a)
81 3 4 × 27 1 = ( 81 4 ) 3 × ( 3 3 ) 1 = ( 3 ) 3 × 3 3 = 3 3 + ( 3 ) = 3 0 = 1

(b)
8 2 3 × 3 2 = ( 8 3 ) 2 × 1 3 2 = ( 2 ) 2 × 1 3 2 = 4 × 1 9 = 4 9


Question 6:
Find the value of the following.
  (a) 16 4 3 × ( 3 2 ) 3 × 9 3 2      
  (b) 2 2 × 3 2 2 3 × 81    

Solution:
(a)
16 4 3 × ( 3 2 ) 3 × 9 3 2 = ( 2 4 ) 4 3 × 3 6 × ( 3 2 ) 3 2 = 2 3 × 3 6 × 3 3 = 2 3 × 3 3 = 8 × 1 3 3 = 8 27  

(b)
2 2 × 3 2 2 3 × 81 = 2 2 × 3 2 2 3 × 3 4 = 2 2 ( 3 ) × 3 2 4 = 2 × 3 2 = 2 3 2 = 2 9


Question 7:
Find the value of the following.
  (a)   (23)2 × 24 ÷ 25
  (b) a 2 × a 1 2 ( a 2 3 × a 1 3 ) 2    

Solution:
(a)
(23)2 × 24 ÷ 25= 26 × 24 ÷ 25
= 26+4-5
= 25
= 32

(b)
a 2 × a 1 2 ( a 2 3 × a 1 3 ) 2 = a 2 + 1 2 ( a 2 3 × a 1 3 ) 2 = a 2 + 1 2 ( a 2 3 + 1 3 ) 2 = a 5 2 a 2 = a 5 2 ( 2 ) = a 5 2 + 4 2 = a 9 2

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