Direction: Study the following questions carefully and choose the right answer.
Important for :
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 × ( c6 a6 ) 2 c8 a–6 b4
» Explain it
A
 ( a4 b6 ) 3 × ( b8 c4 ) –2 × ( c6 a6 ) 2 c8 a–6 b4

 = ( a4×3 b6×3 ) c8×3

 × ( 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.