a)
\frac{5^{\frac{2}{3}}*125^{-\frac{5}{3}}:\sqrt[4]{625^2}*\sqrt[12]{5}}{4*5^{\frac{3}{4}}+5^{\frac{3}{4}}}=
=\frac{5^{\frac{2}{3}}*(5^3)^{-\frac{5}{3}}:((5^4)^2)^{\frac{1}{4}}*5^{\frac{1}{12}}}{5^{\frac{3}{4}}(4+1)}=
=\frac{5^{\frac{2}{3}}*5^{-3}:5^{\frac{8}{4}}*5^{\frac{1}{12}}}{5^{\frac{3}{4}}*5}=
=\frac{5^{\frac{8}{12}}*5^{-\frac{60}{12}}:5^{\frac{24}{12}}*5^{\frac{1}{12}}}{5^{\frac{3}{4}}*5^{\frac{4}{4}}}=
=\frac{5^{\frac{8-60-24+1}{12}}}{5^{\frac{7}{4}}}=\frac{5^{\frac{-75}{12}}}{5^{\frac{21}{12}}}=5^{\frac{-75}{12}-\frac{21}{12}}=5^{\frac{-96}{12}}=5^{-8}
Zadanie 2
\sqrt[3]{100}*5^{\frac{1}{3}}*2^{\frac{4}{3}}=\sqrt[3]{100}*\sqrt[3]{5}*\sqrt[3]{2^4}=\sqrt[3]{100*5*16}=\sqrt[3]{8000}=\sqrt[3]{20^2}=20