Odpowiedź:
[tex]a)\ \ 16^{\frac{5}{12}}\cdot16^{\frac{1}{3}}=16^{\frac{5}{12}+\frac{1}{3}}=16^{\frac{5}{12}+\frac{4}{12}}=16^{\frac{9}{12}}=16^{\frac{3}{4}}=(2^4)^{\frac{3}{4}}=2^3=8\\\\\\b)\ \ 49^{\frac{5}{6}}:49^{\frac{1}{3}}=49^{\frac{5}{6}-\frac{1}{3}}=49^{\frac{5}{6}-\frac{2}{6}}=49^{\frac{3}{6}}=49^{\frac{1}{2}}=(7^2)^{\frac{1}{2}}=7^1=7[/tex]
[tex]c)\ \ (2\frac{2}{9})^{-\frac{2}{3}}\cdot(\frac{2}{15})^{-\frac{2}{3}}=(2\frac{2}{9}\cdot\frac{2}{15})^{-\frac{2}{3}}=(\frac{\not20^4}{9}\cdot\frac{2}{\not15_{3}})^{-\frac{2}{3}}=(\frac{8}{27})^{-\frac{2}{3}}=(\frac{27}{8})^{\frac{2}{3}}=\left(\sqrt[3]{\frac{27}{8}}\right)^2=\\=(\frac{3}{2})^2=\frac{9}{4}=2\frac{1}{4}[/tex]
[tex]d)\ \ 10^{\frac{2}{5}}:(\frac{5}{16})^{\frac{2}{5}}=(10:\frac{5}{16})^{\frac{2}{5}}=(\not10^2\cdot\frac{16}{\not5_{1}})^{\frac{2}{5}}=(2\cdot16)^{\frac{2}{5}}=32^{\frac{2}{5}}=(2^5)^{\frac{2}{5}}=2^2=4\\\\\\e)\ \ ((\frac{8}{27})^{-\frac{4}{5}})^{\frac{5}{6}}=(\frac{8}{27})^{-\frac{2}{3}}=(\frac{27}{8})^{\frac{2}{3}}=\left(\sqrt[3]{\frac{27}{8}}\right)^2=(\frac{3}{2})^2=\frac{9}{4}=2\frac{1}{4}[/tex]
