If n=10^100and n^n=10k what is the value of k?
If n=10^100and n^n=10k what is the value of k?
Answer/Solution
10^102
Steps/Work
There is a simple logic to this question.
(a^m)^n = a^mn
So, (10^100)^(10^100) = 10^(100*(10^100))
= 10^((10^2)*(10^100))
= 10^(10^102)
and this equals 10^k
So, k = 10^102
ANSWER:C
(a^m)^n = a^mn
So, (10^100)^(10^100) = 10^(100*(10^100))
= 10^((10^2)*(10^100))
= 10^(10^102)
and this equals 10^k
So, k = 10^102
ANSWER:C