Odpowiedź i szczegółowe wyjaśnienie:
[tex]a)\ \dfrac{5^{13}\cdot3+2\cdot5^{13}}{(5^{11}:25^4)\cdot 25}=\dfrac{5^{13}(3+2)}{(5^{11}:(5^2)^4)\cdot5^2}=\dfrac{5^{13}\cdot 5}{(5^{11}:5^8)\cdot5^2}=\dfrac{5^{14}}{5^3\cdot5^2}=\\\\=\dfrac{5^{14}}{5^5}=5^{14-5}=5^9\\\\\\b)\ 2^\frac12\cdot50^\frac12-2^\frac15\cdot16^\frac15=(2\cdot50)^\frac12-(2\cdot16)^\frac15=100^\frac12-32^\frac15=\\\\=(10^2)^\frac12-(2^5)^\frac15=10-2=8\\\\\\c)\ \sqrt[3]{-375}-\sqrt[3]{-192}-\sqrt[3]{-81}=\sqrt[3]{-125\cdot3}-\sqrt[3]{-64\cdot3}-\sqrt[3]{-27\cdot3}=\\\\[/tex]
[tex]=\sqrt[3]{(-5)^3\cdot3}}-\sqrt[3]{(-4)^3\cdot3}-\sqrt[3]{(-3)^3\cdot3}=\\\\=-5\sqrt[3]3-(-4\sqrt[3]3)-(-3\sqrt[3]3)=-5\sqrt[3]3+4\sqrt[3]3+3\sqrt[3]3=2\sqrt[3]3\\\\\\d)\ 5^{2+\sqrt3}:5^{3+\sqrt3}=5^{2+\sqrt3-(3+\sqrt3)}=5^{2+\sqrt3-3-\sqrt3}=5^{-1}\\\\\\e)\ log_410+log_4\dfrac25=log_4(10\cdot\dfrac25)=log_44=1[/tex]
