A new number system

It looks like the number system is base 5, although I don't understand why 36 is written as 71 (7×5+1) and not 121 (1×25+2×5+1), which is the normal base 5 representation.

Anyways,

$\frac {11^3}{11^{-1}} = 11^3 \cdot 11^1 = 11^4 = 14641 = \boxed{432031_5}$

The number system Jimmy is using is Base-5. In this system, ordinary numbers (in base ten), are represented, such that each number place represents a power of five. So in the first place, numbers up to four can be represented. When we reach five, it will be 10. When we reach 25, it will be 100. So 11^3, which is 1331, when divided by 0.0909090909, which is 11^-1, gives 14641. 14641, when presented gives 432031.