Question

вычислите:
а)$frac{9^{6}+9 ^{7} }{3^{12}+3^{14}+3^{15}}$

б)$frac{2^{16}-2^{18}+2^{19}}{16^{4}-16^{6}}$

в)$frac{5^{12}-5^{13}-5^{14}-5^{15}}{25^{8}-25^{6}}$

г)$frac{36^{2}+36^{3}}{6^{4}-6^{5}+6^{6}-6^{7}}$

Answer 1

a) $= frac{ 9^{6}(1+9) }{ 3^{12}(1+3 ^{2}+ 3^{3} } = frac{ 9^{6}*10 }{ (3^{2}) ^{6}(1+9+ 27 } = frac{ 9^{6}*10 }{9^{6}*37 }= frac{10}{37}$
б)=$frac{ 2^{16}(1-2^{2}+2^{3} ) }{ 16^{4}(1- 16^{2}) } = frac{ (2 ^{4}) ^{4}(1-4+8 ) }{ 16^{4}(1- 256) }=frac{ 16 ^{4}*5}{ 16^{4}*(- 255) }=- frac{1}{51}$
в)=$frac{ 5^{12}(1-5-5^{2}-5^{3})}{ 25^{6}( 25^{2}-1 } = frac{ (5^{2}) ^{6}(-4-25-125)}{ 25^{6}( 625-1) } = frac{ 25 ^{6}(-154)}{ 25^{6}(624) } =- frac{2*11*7}{8*78} =- frac{77}{312}$
г)$= frac{ 36^{2}(1+36) }{6 ^{4}(1-6+6 ^{2}-6 ^{3} }= frac{ 36^{2}(37) }{36 ^{2}(-5+36-216 )}= frac{37}{-185} = -frac{1}{5}$