Question

ПОМОГИТЕ ПОЖАЛУЙСТА РЕШИТЬ 2 ПРИМЕРА (3,6)

Answer 1

$frac{144^{2m+3}}{6^{4m+4}*4^{2m+3}}= frac{144^{2m}*144^{3}}{6^{4m}*6^{4}*4^{2m}*4^{3}}= frac{144^{2m}*144^{3}}{6^{2*2m}*4^{2m}*6^{4}*4^{3}}= frac{144^{2m}*144^{3}}{36^{2m}*4^{2m}*6*6^{3}*4^{3}}=$

$= frac{(36*4)^{2m}*144^{3}}{(36*4)^{2m}*6*(6*4)^{3}}= frac{144^{3}}{6*(6*4)^{3}}= frac{1}{6}* (frac{144}{6*4} )^3 = frac{1}{6}* (frac{6*6*4}{6*4} )^3= frac{1}{6} * frac{6^3}{1} =$

$=6^{3-1}=6^2=36$
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$(1 frac{7}{9} )^6* frac{6^{15}}{8^{11}} =(frac{1*9+7}{9} )^6* frac{6^{15}}{8^{11}} =(frac{16}{3^2} )^6* frac{6^{15}}{8^{11}} =(frac{2^4}{3^2} )^6* frac{(2*3)^{15}}{(2^3)^{11}} =$

$=frac{2^{4*6}}{3^{2*6}}* frac{2^{15}*3^{15}}{2^{3*11}}=frac{2^{24}}{3^{12}}* frac{2^{15}*3^{15}}{2^{33}}=frac{2^{24}*2^{15}*3^{15}}{3^{12}*2^{33}}=frac{2^{24+15}*3^{15}}{3^{12}*2^{33}} = frac{2^{39}}{2^{33}}* frac{3^{15}}{3^{12}}=$

$=frac{2^{39}}{2^{33}}* frac{3^{15}}{3^{12}}=2^{39-33}*3^{15-12}=2^6*3^3=64*27=1728$