zadanie 38 podpunkt a,b,c,d Wykonaj podane obliczenia
a) \frac{2*5^{20}-5^{18}}{25^9}
b) \frac{(2^{19}+2^{18})*3^2}{(2^{18}+2^{17})*27}
d) \frac{1^{-1}+2^{-1}+3^{-1}}{(\frac{3}{4})}
źródło: zadanie 38 str 62
a) \frac{2*5^{20}-5^{18}}{25^9}=\frac{5^{18}(2*5^2-1)}{(5^2)^9}=\frac{5^{18}*49}{5^{18}}=49 b) \frac{(2^{19}+2^{18})*3^2}{(2^{18}+2^{17})*27}=\frac{2^{18}(2+1)*9}{2^{17}(2+1)*27}=\frac{2^{18-17}}{3}=\frac{2}{3} c) [{(1\frac{1}{2})^{-1}-3^{-2}]^{-2}}=[(\frac{3}{2})^{-1}-\frac{1}{3^2}]^{-2}=(\frac{2}{3}-\frac{1}{9})^{-2}=(\frac{6}{9}-\frac{1}{9})^{-2}=(\frac{5}{9})^{-2}=(\frac{9}{5})^{2}=\frac{81}{25}=3\frac{6}{25}
d) \frac{1^{-1}+2^{-1}+3^{-1}}{(\frac{3}{4})^{-1}+3^{-1}*2}=\frac{1+\frac{1}{2}+\frac{1}{3}}{\frac{4}{3}+\frac{1}{3}*2}=\frac{\frac{6+3+2}{6}}{\frac{6}{3}}=\frac{11}{6}:2=\frac{11}{6}*\frac{1}{2}=\frac{11}{12}
\frac{1^{-1}+2^{-1}+3^{-1}}{(\frac{3}{4})+3^{-1}*2}=\frac{1+\frac{1}{2}+\frac{1}{3}}{}