Question

ПОМОГИТЕ пожалуйста решить 2 примера(1,4)!

Answer 1

$frac{4^{4m-5}*( frac{1}{6} )^{-2m}}{96^{2m-3}} = frac{4^{(4m-4)+(-1)}*( frac{6}{1} )^{2m}}{96^{2m-3}} = frac{4^{4m-4}*4^{-1}*6^{2m}}{(16*6)^{2m-3}} =$

$=frac{4^{2(2m-2)}*4^{-1}*6^{2m}}{(16*6)^{2m-3}}=frac{16^{2m-2}*4^{-1}*6^{2m}}{(16*6)^{2m-3}} =frac{16^{2m}*6^{2m}*16^{-2}*4^{-1}*6^{2m}}{(16*6)^{2m-3}} =$

$=frac{(16*6)^{2m}*16^{-2}*4^{-1}}{(16*6)^{2m}*96^{-3}}=frac{16^{-2}*4^{-1}}{96^{-3}}=frac{16^{-2}*4^{-1}*96^3}{1}=frac{(16*6)^3}{16^2*4} =$

$=frac{16^3*6^3}{16^2*4} = frac{16^1*36*6}{4} = frac{4*216}{1} =864$

$frac{24^{k+1}}{128*4^{k-1}*6^{k-2}}=frac{24^{k}*24}{128*4^{k}*4^{-1}*6^{k}*6^{-2}}=frac{24^{k}*24}{4^{k}*6^k*128* frac{1}{4}* frac{1}{6^2} }}=frac{24^{k}*24}{(4*6)^{k}*frac{128}{4*36}}}=$

$=frac{(4*6)^{k}*24}{(4*6)^{k}*frac{4*4*8}{4*4*9}}} =frac{8*3}{frac{8}{9}}}= frac{8*3*9}{8} =3*9=27$