We　conduct　a　mathematical　investigation　into　the　dynamical　stability　and　instability　of　the　Rayleigh-Benard　(abbr.　RB)　problem　for　incompressible　non-Newtonian　fluids　exhibiting　power　law　type　behavior,　with　p　＞=　1.　We　establish　a　critical　threshold,　denoted　as　R-c,　and　endeavor　to　demonstrate　that　the　RB　problem　exhibits　exponential　stability　through　the　energy　method　when　the　Rayleigh　number　R　(which　is　influenced　by　the　non-Newtonian　component)　falls　within　the　interval　[0,　R-c).　Additionally,　we　formulate　an　instability　criterion,　R　＞　R-c,　under　which　the　RB　problem　is　deemed　unstable,　we　aim　to　prove　this　instability　by　employing　a　modified　variational　method.　Our　results　show　that　non-Newtonian　part　has　the　stabilizing　effect　for　thermal　instability.