Question

for what value of n where n is a natural number is:

1). (24)^n is divisible by 8

2). (18)^n is divisible by 6

3). (19)^n is divisible by 9
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Answer 1

Answer:

for any value of n such that n is a natural number (1) (24)^n is divisible by n as we can express (24)^n as (4×6)^n => 4^n ×6^n hence it is divisible by 6 as 6 is a factor of it

similarly in (2) 18^n is also divisible for any value of n =>18^n = 3^n ×6^n

(3) 19^n can't be divisible by 9 as on expansion it can be written as 19×19×19×19×19..... n times Hope it helps you.