Answer:
1
Step-by-step explanation:
The given ratio will be the remaining factor of 343 after factors of 7 have been removed. The value of interest is that factor, modulo 7.
Factors of 343
343 = 7·7·7 = 7³
Ratio
The value of k is the power of 7 in the factorization of 343, so we have ...
k = 3
and ...
343/7³ = 1
Remainder
The remainder when this ratio is divided by 7 is ...
1 mod 7 = 1
The remainder when 343/7^k is divided by 7 is 1.
