Odpowiedź:
[tex]a)\ \ 3^3\cdot27^{-\frac{4}{3}}=3^3\cdot(3^3)^{-\frac{4}{3}}=3^3\cdot3^{-4}=3^{3-4}=3^{-1}=(\frac{1}{3})^1=\frac{1}{3}\\\\\\b)\ \ 2^{\frac{1}{2}}\cdot4^{\frac{3}{2}}:8^{\frac{2}{3}}=2^{\frac{1}{2}}\cdot(2^2)^{\frac{3}{2}}:(2^3)^{\frac{2}{3}}=2^{\frac{1}{2}}\cdot2^3:2^2=2^{\frac{1}{2}+3-2}=2^{\frac{1}{2}+1}=2^{\frac{3}{2}}=\sqrt{2^3}=\\\\=\sqrt{8}=\sqrt{4\cdot2}=2\sqrt{2}[/tex]
[tex]c)\ \ (3^{\sqrt{7}-3})^{\sqrt{7}+3}=3^{(\sqrt{7}-3)(\sqrt{7}+3)}=3^{(\sqrt{7})^2-3^2}=3^7-9}=3^{-2}=(\frac{1}{3})^2=\frac{1}{9}\\\\\\d)\ \ (5^{\sqrt{3}-1})^{\sqrt{3}+1}=5^{(\sqrt{3}-1)(\sqrt{3}+1)}=5^{(\sqrt{3})^2-1^2}=5^{3-1}=5^2=25[/tex]
