Direction: Study the following questions carefully and choose the right answer.
1
The number of prime factors in 6333 × 7222 × 8111
» Explain it
A
(6)333 × (7)222 × (8)111

∴   (2 × 3)333 × (7)222 × (23)111

   2333 × 3333 × 7222 × 2333

   2666 × 3333 × 7222

    Number of prime factors

= 666 + 333 + 222 = 1221.

Hence, option A is correct.

2
Simplify  ( 1 ) 0  + (64)–1/2 + (–32)4/5
64  
» Explain it
A
  ( 1 ) 0  + (64)–1/2 + (–32)4/5
64  

= 1 + (82)–1/2 + (–1 × 32)4/5

= 1 +  1  + [(–12)2/5 × (25)4/5]
8

= 1 +  1  + [24] = 17 1 .
8 8

Hence, option A is correct.

3
Simplify:  ( 256 ) 1/4  ×  ( 64 ) –1/3  ×  ( 216 ) –1
576   27   8  
» Explain it
B
As 256 = 28;   576 = 242;   64 = 26;   27 = 33

  ( 256 ) 1/4  ×  ( 64 ) –1/3  ×  ( 216 ) –1
576   27   8  

  ( 28 ) 1/4  ×  ( 33 ) 1/3  ×  ( 8 )
242   26   216

=   22  ×  3  ×  1  =  1  =  1
24 4 27
2 6  × 9
18  6

Hence, option B is correct.

4
Simplify the following    ( a4 b6 ) 3  ×  ( b8 c4 ) –2  ×  ( ca6 ) 2
c8   a–6   b4  
» Explain it
A
( a4 b6 ) 3  ×  ( b8 c4 ) –2  ×  ( ca6 ) 2
c8   a–6   b4  

=   ( a4×3 b6×3 )
c3

 ×  ( b8×(–2) c4×(–2) )
a–6×(–2)

 ×  ( c6×2 a6×2 )
b4×2

= a12–12+12   b18–16–8 c–8+12–24 

a12
b6. c20

Hence, option A is correct.

5
( 216 ) –2/3  ÷  ( 27 ) –4/3  = ?
1   1  
» Explain it
B
Putting x for (?) , we get

( 216 ) –2/3  ÷  ( 27 ) –4/3  = x
1   1  

x =  ( 1 ) 2  ÷  ( 1 ) 4
6   3  

 =  1  ÷  1  =  1  ×  81
36 81 36 1

⇒ x =  81  =  9
36 4

Hence, option B is correct.