  The persistent tensions between inclusive and exclusive determinations of
$|V_{cb}|$ and $|V_{ub}|$ weaken the power of theoretically clean rare $K$ and
$B$ decays in the search for new physics (NP). We demonstrate how this
uncertainty can be practically removed by considering within the SM suitable
ratios of various branching ratios. This includes the branching ratios for
$K^+\to\pi^+\nu\bar\nu$, $K_{L}\to\pi^0\nu\bar\nu$, $K_S\to\mu^+\mu^-$,
$B_{s,d}\to\mu^+\mu^-$ and $B\to K(K^*)\nu\bar\nu$. Also $\epsilon_K$, $\Delta
M_d$, $\Delta M_s$ and the mixing induced CP-asymmetry $S_{\psi K_S}$, all
measured already very precisely, play an important role in this analysis. The
highlights of our analysis are 16 $|V_{cb}|$ and $|V_{ub}|$ independent ratios
that often are independent of the CKM arameters or depend only on the angles
$\beta$ and $\gamma$ in the Unitarity Triangle with $\beta$ already precisely
known and $\gamma$ to be measured precisely in the coming years by the LHCb and
Belle II collaborations. Once $\gamma$ Once $\gamma$ is measured precisely
these 16 ratios taken together are expected to be a powerful tool in the search
for new physics. Assuming no NP in $|\epsilon_K|$ and $S_{\psi K_S}$ we
determine independently of $|V_{cb}|$:
$\mathcal{B}(K^+\to\pi^+\nu\bar\nu)_\text{SM}= (8.60\pm0.42)\times 10^{-11}$
and $\mathcal{B}(K_L\to\pi^0\nu\bar\nu)_\text{SM}=(2.94\pm 0.15)\times
10^{-11}$. This are the most precise determinations to date. Assuming no NP in
$\Delta M_{s,d}$ allows to obtain analogous results for all $B$ decay branching
ratios considered in our paper without any CKM uncertainties.
