Minerals such as zircon are routinely used by geochronologists to confidently provide the U-Pb and Pb-Pb ages which underpin the conventional multi-millions-of-years' time scale. These dating methods and the underlying assumptions are reviewed. It is then documented from the conventional literature that both U and Pb isotopes naturally mass fractionate due to the nuclear-field shift effect and differential mass diffusion. Furthermore, the beams used in the instruments to sample tiny volumes of such minerals for their mass spectrometer isotopic analyses also cause isotopic mass fractionation, especially of Pb isotopes. Much effort has thus been expended in the conventional geochronology community to quantify the amounts of fractionation the various beams induce so that appropriate uncertainties can be stipulated for the obtained U-Pb and Pb-Pb dates. However, all such efforts involve the use of standards of "known" ages determined by U-Pb, Pb-Pb and /or other radiometric methods such as K-Ar or Ar-Ar. This is circular reasoning, especially compounded by the decay constants of all the other parent isotopes used for dating the standards having been calibrated against the 238U decay constant. Yet the uncertainties are still significant and are compounded further by the uncertainties in the measured 238U and 235U decay rates, the crucial 238U/235U ratio, the amount and composition of inherited, initial and/or common Pb, and the possibility of both U and Pb mobility after minerals and the rocks containing them were formed. Thus, the resultant U-Pb and Pb-Pb ages obtained are subjective and only provide systematic relative ages, even though geochronologists take numerous precautions to make the U-Pb and Pb-Pb methods still have a strong aura of validity. Yet all these uncertainties are overshadowed by the underlying unprovable assumptions on which the radioisotope dating methods are based, especially the assumption of time-invariant decay rates, built on the foundation of an assumed deep time history. Instead, the evidence for grossly accelerated radioisotope decay during a past cataclysmic event such as the Genesis Flood has been well established. Therefore, those absolute ages cannot be used to dismiss the history of the earth and its approximately 6,000-year chronology provided in God's infallible Word.