Odpowiedź:
[tex]a)\ \ \dfrac{5^{-8}\cdot(5^{-3}:5)^{-1}}{5^6:(5^3\cdot5^6)}=\dfrac{5^{-8}\cdot(5^{-3-1})^{-1}}{5^6:5^{3+6}}=\dfrac{5^{-8}\cdot(5^{-4})^{-1}}{5^6:5^9}=\dfrac{5^{-8}\cdot5^4}{5^{6-9}}=\dfrac{5^{-8+4}}{5^{-3}}=\\\\=\dfrac{5^{-4}}{5^{-3}}=5^{-4-(-3)}=5^{-4+3}=5^{-1}=\frac{1}{5}[/tex]
[tex]b)\ \ \sqrt{6\cdot15^2+15\cdot15+2\cdot15^2}=\sqrt{6\cdot15^2+15^2+2\cdot15^2}=\sqrt{15^2(6+1+2)}=\\\\=\sqrt{15^2\cdot9}=\sqrt{15^2}\cdot\sqrt{9}=15\cdot3=45\\\\\\c)\ \ \sqrt{144\cdot16}=\sqrt{144}\cdot\sqrt{16}=12\cdot4=48\\\\\\d)\ \ \dfrac{2\sqrt{32}+\sqrt{2}}{\sqrt{2}}=\dfrac{2\sqrt{16\cdot2}+\sqrt{2}}{\sqrt{2}}=\dfrac{2\cdot4\sqrt{2}+\sqrt{2}}{\sqrt{2}}=\dfrac{8\sqrt{2}+\sqrt{2}}{\sqrt{2}}=\dfrac{9\sqrt{2}}{\sqrt{2}}=9[/tex]
[tex]e)\ \ \sqrt[3]{3}\cdot\sqrt[3]{9}+\sqrt{50}\cdot\sqrt{2}=\sqrt[3]{3\cdot9}+\sqrt{50\cdot2}=\sqrt[3]{27}+\sqrt{100}=3+10=13\\\\\\f)\ \ 5\sqrt{3}+3\sqrt{12}+5\sqrt{27}=5\sqrt{3}+3\sqrt{4\cdot3}+5\sqrt{27\cdot3}=5\sqrt{3}+3\cdot2\sqrt{3}+5\cdot3\sqrt{3}=\\\\=5\sqrt{3}+6\sqrt{3}+15\sqrt{3}=26\sqrt{3}[/tex]
[tex]g)\ \ (3\sqrt{2})^2+(4\sqrt{3})^2-(\sqrt{11})^2=3^2\cdot(\sqrt{2})^2+4^2\cdot(\sqrt{3})^2-11=9\cdot2+16\cdot3-11=\\\\=18+48-11=66-11=55[/tex]
