  In this note, we are interested in obtaining uniform upper bounds for the
number of powerful numbers in short intervals $(x, x + y]$. We obtain
unconditional upper bounds $O(\frac{y}{\log y})$ and $O(y^{11/12})$ for all
powerful numbers and $y^{1/2}$-smooth powerful numbers respectively.
Conditional on the $abc$-conjecture, we prove the bound
$O(\frac{y}{\log^{1+\epsilon} y})$ for squarefull numbers and the bound
$O(y^{(2 + \epsilon)/k})$ for $k$-full numbers when $k \ge 3$. They are related
to Roth's theorem on arithmetic progressions and the conjecture on
non-existence of three consecutive squarefull numbers.
