The problem is the same as in What makes my line get shifted to the left when I invoke \LoadConstants? and the solution again the same: add
\makeatletter
\def\FP@pow#1#2#3{% <---- This was unprotected
% #1 macro, which gets the result
% #2 base
% #3 exponent
%
\FP@beginmessage{POW}%
%
{\def\FP@beginmessage##1{}%
\def\FP@endmessage##1{}%
%
\FPifzero{#2}%
\FP@pow@zero{#3}%
\else%
\FPln\FP@tmpd{#2}%
\FPmul\FP@tmpd\FP@tmpd{#3}%
\FPexp\FP@tmp\FP@tmpd%
\fi%
%
\global\let\FP@tmp\FP@tmp%
}%
%
\FP@endmessage{}%
%
\let#1\FP@tmp%
}
\makeatother
before \begin{document}.
Here's a four row spreadtab after the change:
\documentclass{standalone}
\usepackage{spreadtab}
\makeatletter
\def\FP@pow#1#2#3{% <---- This was unprotected
% #1 macro, which gets the result
% #2 base
% #3 exponent
%
\FP@beginmessage{POW}%
%
{\def\FP@beginmessage##1{}%
\def\FP@endmessage##1{}%
%
\FPifzero{#2}%
\FP@pow@zero{#3}%
\else%
\FPln\FP@tmpd{#2}%
\FPmul\FP@tmpd\FP@tmpd{#3}%
\FPexp\FP@tmp\FP@tmpd%
\fi%
%
\global\let\FP@tmp\FP@tmp%
}%
%
\FP@endmessage{}%
%
\let#1\FP@tmp%
}
\makeatother
\begin{document}
\begin{spreadtab}{{tabular}{lll}}
\STcopy{>,v}{pow(1,1)}
& &
\\
& &
\\
& &
\\
& &
\end{spreadtab}
\end{document}

Elementary, Watson.
How to find the source of the spurious spaces?
I added \tracingcommands=1 \tracingmacros=1 before \begin{spreadtabs} and run LaTeX. Then looked for {blank space} in the log file. Look and behold!
\FP@pow #1#2#3-> \FP@beginmessage {POW}{\def \FP@beginmessage ##1{}\def \FP@end
message ##1{}\FPifzero {#2}\FP@pow@zero {#3}\else \FPln \FP@tmpd {#2}\FPmul \FP
@tmpd \FP@tmpd {#3}\FPexp \FP@tmp \FP@tmpd \fi \global \let \FP@tmp \FP@tmp }\F
P@endmessage {}\let #1\FP@tmp
#1<-\FP@valc
#2<-\FP@vala
#3<-\FP@valb
{blank space }
\FP@beginmessage #1->\ifFPmessages \message {( FP-#1}\fi
#1<-POW
{begin-group character {}
{\def}
{\def}
The space was added in the middle of expanding \FP@pow. Where did I see that? Oh, yes! The old question I referenced. Problem solved.
Well, it's the same problem, so I made the answer “community wiki”. Otherwise some respected user could insinuate I get my rep just by chasing missing %.
fppackage got updated in January 2019 and the patch is no longer needed. – egreg Jan 22 '19 at 10:11