Smallest Or Biggest Number amongst Exponential Numbers
Q) Prelims 2022 --> Which number among 240 , 321 , 418 , and 812 is smallest ?
a) 240
b) 321
c) 418
d) 812
Solution :-
Category:- Quantitative Aptitude --> Basic Concept --> Laws of Indices
Common Strategies :-
1) Common Base
2) Common Exponent
Solving by both Common Exponent method and Common Base method
HCF of 21 , 18 and 12 is 3
--> 21 can be rewritten as 3 x 7 , hence, (37)3= (3x3x3x3x3x3x3)3= (2187)3
--> 18 can be rewritten as 3 x 6 , hence, (46)3= (4x4x4x4x4x4)3= (4096)3
--> 12 can be rewritten as 3 x 4 , hence, (84)3= (8x8x8x8)3= (4096)3
240 can be written as 2 x (23)13= 2 x 813 by common base method it is greater than 812 Hence Out of Option
so from above three Exponents the smallest value is (2187)3 Hence correct option is (b)