1.2.2 Indices, PT3 Practice


Question 6:
Find the value of the following.
  (a) 8 4 3 × ( 3 2 ) 3 × 9 3 2  
  (b) 2 2 × 3 2 2 3 × 81    

Solution:
(a)
8 4 3 × ( 3 2 ) 3 × 9 3 2 = ( 2 3 ) 4 3 × 3 6 × ( 3 2 ) 3 2 = 2 4 × 3 6 × 3 3 =16× 3 6+3 =16× 3 3 =16× 1 3 3 = 16 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:
Given that 2 8x =32 , calculate the value of x.

Solution:
2 8x =32 2 8x =2 5 8x=5 x=3 x=3

Question 8:
Given  3 2p1 =( 3 p )( 3 2 ), calculate the value of p.

Solution:
3 2p1 =( 3 p )( 3 2 ) 3 2p1 = 3 p+2 2p1=p+2 p=3

Question 9:
Given that 8× 8 p+1 =( 8 5 )( 8 3 ), find the value of p.

Solution:
8× 8 p+1 =( 8 5 )( 8 3 ) 8 1+p+1 = 8 5+3 2+p=8 p=6

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