  The $k$-power domination problem is a problem in graph theory, which has
applications in many areas. However, it is hard to calculate the exact
$k$-power domination number since determining k-power domination number of a
generic graph is a NP-complete problem. We determine the exact $k$-power
domination number in two graphs which have the same number of vertices and
edges: pseudofractal scale-free web and Sierpi\'nski gasket. The $k$-power
domination number becomes 1 for $k\ge2$ in the Sierpi\'nski gasket, while the
$k$-power domination number increases at an exponential rate with regard to the
number of vertices in the pseudofractal scale-free web. The scale-free property
may account for the difference in the behavior of two graphs.
