a)
(\frac{1}{2})^4+(1\frac{3}{4})^2=((\frac{1}{2})^2)^2+(\frac{7}{4})^2=(\frac{1}{4})^2+(\frac{7}{4})^2=\frac{1}{16}+\frac{49}{16}=\frac{50}{16}=\frac{25}{8}=3\frac{1}{8}
b)
(\frac{2}{3})^3*(2,25)^2=\frac{8}{27}*(2\frac{1}{4})^2=\frac{8}{27}*(\frac{9}{4})^2=\frac{8}{27}*\frac{81}{16}=\frac{3}{2}=1\frac{1}{2}
sprawdzenie http://www.wolframalpha.com/input/?i=%28\frac{2}{3}%29^3*%282.25%29^2
c)
\sqrt[3]{\frac{1}{27}}+\sqrt{1\frac{13}{36}}=\sqrt[3]{\frac{1}{3^3}}+\sqrt{\frac{49}{36}}=\frac{1}{3}+\frac{7}{6}=\frac{2+7}{6}=\frac{9}{6}=1\frac{3}{6}=1\frac{1}{2}
d)
(\frac{3}{4})^{-1}-(2,7)^0=\frac{4}{3}-1=1\frac{1}{3}-1=\frac{1}{3}
e)
\sqrt{2-\frac{1}{25}}-\sqrt{1-0,99}=\sqrt{\frac{50}{25}-\frac{1}{25}}-\sqrt{0,01}=\sqrt{\frac{49}{25}}-\sqrt{0,1^2}=\frac{7}{5}-\frac{1}{10}=\frac{14}{10}-\frac{1}{10}=\frac{13}{10}=1\frac{3}{10}=1,3
f)
(1\frac{1}{9})^{-1}:(1\frac{2}{3})^{-2}=(\frac{10}{9})^{-1}:(\frac{5}{3})^{-2}=\frac{9}{10}:(\frac{3}{5})^2=\frac{9}{10}:\frac{9}{25}=\frac{9}{10}*\frac{25}{9}=\frac{5}{2}=2,5