Odpowiedź:
[tex]a)\ \ 2\cdot16^{-1,5}\cdot32^{1,2}=2\cdot(2^4)^{-1,5}\cdot(2^5)^{1,2}=2\cdot2^{-6}\cdot2^6=2^{1+(-6)+6}=\\\\=2^{1-6+6}=2^1=2\\\\\\b)\ \ 5^{-3}\cdot125^{\frac{2}{3}}\cdot625^{\frac{5}{4}}=5^{-3}\cdot(5^3)^{\frac{2}{3}}\cdot(5^4)^{\frac{5}{4}}=5^{-3}\cdot5^2\cdot5^5=5^{-3+2+5}=5^4=625[/tex]
[tex]c)\ \ [(\frac{16}{49})^{\frac{-3}{2}}\cdot(\frac{7}{4})^{\frac{2}{5}}\cdot(\frac{4}{7})^{\frac{-3}{5}}]^{\frac{1}{4}}=[(\frac{16}{49})^{-\frac{3}{2}}\cdot(\frac{4}{7})^{-\frac{2}{5}}\cdot(\frac{4}{7})^{-\frac{3}{5}}]^{\frac{1}{4}}=[((\frac{4}{7})^2)^{-\frac{3}{2}}\cdot(\frac{4}{7})^{-\frac{2}{5}-\frac{3}{5}}}]^{\frac{1}{4}}=[/tex]
[tex]=[(\frac{4}{7})^{-3}\cdot(\frac{4}{7})^{-1}]^{\frac{1}{4}}=[(\frac{4}{7})^{-3-1}]^{\frac{1}{4}}=[(\frac{4}{7})^{-4}]^{\frac{1}{4}}=(\frac{4}{7})^{-1}=(\frac{7}{4})^1=\frac{7}{4}=1\frac{3}{4}[/tex]
[tex]d)\ \ (3^{\frac{1}{3}}\cdot27^{\frac{2}{3}}\cdot3^{-2})^{\frac{3}{-4}}=(3^{\frac{1}{3}}\cdot(3^3)^{\frac{2}{3}}\cdot3^{-2})^{-\frac{3}{4}}=(3^{\frac{1}{3}}\cdot3^2\cdot3^{-2})^{-\frac{3}{4}}=(3^{\frac{1}{3}+2-2})^{-\frac{3}{4}}=\\\\=(3^{\frac{1}{3}})^{-\frac{3}{4}}=3^{-\frac{1}{4}}[/tex]
