Odpowiedź:
[tex]a)\ \ (3^{-2})^{-3}:3^8=3^{-2\cdot(-3)}:3^8=3^6:3^8=3^{6-8}=3^{-2}=(\frac{1}{3})^2=\frac{1}{9}\\\\\\b)\ \ (4^{-5})^{-2}:4^9=4^{-5\cdot(-2)}:4^9=4^{10}:4^9=4^{10-9}=4^1=4\\\\\\c)\ \ (5^{-1})^{-3}:5^6=5^{-1\cdot(-3)}:5^6=5^3:5^6=5^{3-6}=5^{-3}=(\frac{1}{5})^3=\frac{1}{125}\\\\\\d)\ \ (2^2)^{-4}:2^{-6}=2^{2\cdot(-4)}:2^{-6}=2^{-8}:2^{-6}=2^{-8-(-6)}=2^{-8+6}=2^{-2}=\\\\=(\frac{1}{2})^2=\frac{1}{4}[/tex]
[tex]e)\ \ [(\frac{4}{3})^{-2}]^2\cdot(\frac{4}{3})^6=(\frac{4}{3})^{-4}\cdot(\frac{4}{3})^6=(\frac{4}{3})^{-4+6}=(\frac{4}{3})^2=\frac{16}{9}=1\frac{7}{9}\\\\\\f)\ \ [(2\frac{1}{5})^{-3}]^3\cdot(2\frac{1}{5})^7=(2\frac{1}{5})^{-9}\cdot(2\frac{1}{5})^7=(2\frac{1}{5})^{-9+7}=(\frac{11}{5})^{-2}=(\frac{5}{11})^2=\frac{25}{121}[/tex]
[tex]g)\ \ [(4,2)^{-1}]^{-8}\cdot(4,2)^{-6}=4,2^{8}\cdot4,2^6=4,2^{8-6}=4,2^2=(\frac{42}{10})^2=(\frac{21}{5})^2=\frac{441}{25}=\\\\=17\frac{16}{25}\\\\\\h)\ \ [(3,4)^{-5}]^{-4}\cdot(3,4)^{-21}=3,4^{20}\cdot3,4^{-21}=3,4^{20-21}=3,4^{-1}=(\frac{34}{10})^{-1}=\\\\=(\frac{17}{5})^{-1}=\frac{5}{17}[/tex]
