Q:

What's the pattern? roots and powers of n?

I won't hold it against anyone if this is considered a bad question but I just don't know how else to put it and really want to know.
1st case:
n = positive integer
a = $\sqrt n$
b = 1
2nd case:
n = positive integer
a = $b^2$
b = $\sqrt[3]n$
c = 1
With each new case a new variable is included which is always 1.
I'm assuming the third case must look something like this:
3rd case: 
n = positive integer 
a = $b^2$ 
b = $c^3$ 
c = $\sqrt[4]n$ 
d = 1
But that doesn't work as a ends up larger than n. 
All are supposed to be smaller than n and a letter which comes after another alphabetically should have a value smaller than or equal to.
There is definitely a pattern but I can't pin it down.

A:

The 1st case is $n^1, n^{1/2}, n^0$.
The 2nd case is $n^1, n^{2/3}, n^{1/3}, n^0$.
The 3rd case should presumably be $n^1, n^{3/4}, n^{1/2}, n^{1/4}, n^0$.

