Question

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Answer 1

 

$\displaystyle\bf\\ 5)\\a)~\frac{2}{3},\frac{4}{3},\frac{7}{3},\frac{8}{3},\frac{13}{3},\frac{14}{3}\\\\b)~\frac{7}{11},\frac{8}{11},\frac{10}{11},\frac{11}{11},\frac{12}{11},\frac{15}{11}\\\\6)\\a)~\frac{552}{5},\frac{525}{5},\frac{522}{5},\frac{255}{5},\frac{252}{5},\frac{225}{5}\\\\b)\\8^{20}=(2^3)^{20}=2^{3\times20}=2^{60}\\32^{12}=(2^5)^{12}=2^{5\times12}=2^{60}\\4^{30}=(2^{2})^{30}=2^{2\times30}=2^{60}\\64^{10}=(2^{6})^{10}=2^{6\times10}=2^{60}\\16^{15}=(2^{4})^{15}=2^{4\times15}=2^{60}$

 

$\displaystyle\bf\\\text{Toti numaratorii fractiilor sunt egali cu }~2^{60}\\\\ \frac{2^{60}}{2009},\frac{2^{60}}{2010},\frac{2^{60}}{2011},\frac{2^{60}}{2012},\frac{2^{60}}{2013},\frac{2^{60}}{2014}\\\\c)\\\\9^{29}=3^{58}\\81^{15}=3^{60}\\27^{21}=3^{63}\\243^{13}=3^{65}\\\\\frac{9^{29}}{2013},\frac{3^{59}}{2013},\frac{81^{15}}{2013},\frac{27^{21}}{2013},\frac{243^{13}}{2013}$