  Let $I$ be an equidimensional ideal of a ring polynomial $R$ over
$\mathbb{C}$ and let $J$ be its generic linkage. We prove that there is a
uniform bound of the difference between the F-pure thresholds of $I_p$ and
$J_p$ via the generalized Frobenius powers of ideals. This provides evidence
that the F-pure threshold of an equidimensional ideal $I$ is less than that of
its generic linkage. As a corollary we recover a result on log canonical
thresholds of generic linkage by Niu.
