Directions: Study the following questions carefully and choose the right answer:
1
The value of (256)5/4 is :
» Explain it
C
From the given equation :

(256) 5/4  

= (445/4

= 4(4 × 5/4)  

45 

= 1024.

Hence, option C is correct.

2
1  +  1  +  1  =
(216)−2/3 (256)−3/4 (32)−1/5
» Explain it
A
Given expression =

1  +  1  +  1
(216)−2/3 (256)−3/4 (32)−1/5

1 + 1 + 1
63×(–2/3)
44×(–3/4)
25×(–1/5)

= 1  +  1  +  1
6–2
4–3 
2–1 

= (62 + 43 + 21)

= (36 + 64 + 2)

= 102.

Hence, option A is correct.

3
(2.4 × 103÷ (8 × 10–2) = ?
» Explain it
B
Given equation

= (2.4 × 103) ÷ (8 × 10–2

then,   2.4 × 103
8 × 10– 2

=   24 ×102
8 × 10– 2

=  (3 × 104)

Hence, option B is correct.

4
( 1 ) –2/3 ÷    ( 1 ) –4/3  = ?
216   27  
» Explain it
C
Given equation:

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

(216)(2/3) ÷ (27)(4/3)

= (216)2/3  =   (63)×(2/3) .
(27)4/3 (33)×(4/3)

62  =  36  =  4  
34 81 9

Hence, option C is correct.

5
(1000)7    ÷    1018    = ?  
» Explain it
C
Given equation =  (1000)7    ÷    1018   .

⇒   (1000)7   ⇒   (103)7   ⇒   10(3 × 7) .
(10)18 (10)18 (10)18

⇒   1021   = 10(21 - 18)    103  = 1000.
(10)18

Hence, option C is correct.