Help with this problem please.

[summertime]

Can someone please explain this problem to me:

((1/4)^18 * (1/5)^M) = 1/2(10)^35, what is m.

The answer is 35, but how did they arrive at that answer.

Another question:

At a certain university, the ratio of the number of teaching assistants to the number of student in any course must always be greater than 3:80. At this university, what is the maximum number of students possible in a course that has 5 teaching assistants?

The answer is 133, how did they arrive at this answer because I got 130.

[tohellandback]

your first question:
((1/4)^18 * (1/5)^M) = 1/2(10)^35
1/2(10)^35=1/2(2*5)^35
=1/(2^36*5^35)
=(1/4)^18*(1/5)^35
so M=35

your 2nd question
ratio must be greater than 3:80
Since we have 5 teaching assistants, let's convert numerator to 5
3/80= (3*5/3)/(80*5/3) --we can multiply the numerator and denominator with same constant

=5/(400/3)= 5/133.333..
now we want it to be greater than 3/80, so we sud round up the denominator to 133 and not to 134
answer is 133