Odpowiedź:
[tex]a)\ \ (2,25)^7\cdot(\frac{2}{3})^{15}=(\frac{225}{100})^7\cdot(\frac{2}{3})^{15}=(\frac{9}{4})^7\cdot(\frac{2}{3})^{15}=((\frac{3}{2})^2)^7\cdot(\frac{3}{2})^{-15}=\\\\=(\frac{3}{2})^{14}\cdot(\frac{3}{2})^{-15}=(\frac{3}{2})^{14-15}=(\frac{3}{2})^{-1}=\frac{2}{3}\\\\\\b)\ \ (\frac{1}{3})^6\cdot6^5=\frac{1}{3}\cdot(\frac{1}{3})^5\cdot6^5=\frac{1}{3}\cdot(\frac{1}{\not3_{1}}\cdot\not6^2)^5=\frac{1}{3}\cdot2^5=\frac{1}{3}\cdot32=\frac{32}{3}=10\frac{2}{3}[/tex]
[tex]c)\ \ 4^5\cdot(\frac{3}{8})^4=4\cdot4^4\cdot(\frac{3}{8})^4=4\cdot(\not4^1\cdot\frac{3}{\not8_{2}})^4=4\cdot(\frac{3}{2})^4=\not4^1\cdot\frac{81}{\not16_{4}}=\frac{81}{4}=20\frac{1}{4}\\\\\\d)\ \ (3,75)^3\cdot(\frac{4}{5})^4=(3\frac{3}{4})^3\cdot(\frac{4}{5})^3\cdot\frac{4}{5}=(3\frac{3}{4}\cdot\frac{4}{5})^3\cdot\frac{4}{5}=(\frac{\not15^3}{\not4_{1}}\cdot\frac{\not4^1}{\not5_{1}})^3\cdot\frac{4}{5}=3^3\cdot\frac{4}{5}=\\\\=27\cdot\frac{4}{5}=\frac{108}{5}=21\frac{3}{5}[/tex]
