postgres arithmetic: raising to nth power

[Using postgres (PostgreSQL) 7.4.7 on
GNU/Linux  2.4.27-1-386 - Debian/Sarge]
----------------------------------------

Hi all,
testing a few arithmetic calculations to make sure I understood how
they worked before including them in a a query I met with the following
results:

 select 100*1.10^1277/365::float:     # supposedly: first calculates 1.10^1277
----------------------------------    # then multiplies by 100 and divide by 365
             1.97772581606028e+52
(1 row)

# Let's see if my guess is correct:

 select 100*(1.10)^1277
----------------------
 7.21869922862002e+54
(1 row)

 select 7.21869922862002/365
-----------------------------
      0.01977725816060279452
(1 row)

# Hmmm: same result, except there is no multiplication by 100!

 select 7.21869922862002/365::float
------------------------------------
                 0.0197772581606028
(1 row)

# the presence of either float or numeric dowsn't alter the result.

 select 100*(1.10)^1277::float
-------------------------------
   7.21869922862002e+54
(1 row)

# However, using more reasonable numbers:

 select (1.10)^12
------------------
   3.138428376721
(1 row)

 select 100*(1.10)^12
----------------------
       313.8428376721
(1 row)

the result is correct.
-------------------------------------

So, the problem is: how can I get to know which results are correct and
which aren't?  May be the presence on the trailing 'e+..' is signalling
there is an error?
Could somebody give me a short explanation or suggest further readings?

Thanks for your attention.
Regards,
    Ennio.

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