Odpowiedź:
[tex]\huge\boxed{a)\ 3^{\frac{53}{30}}}\\\boxed{b)\ 5^9}[/tex]
Szczegółowe wyjaśnienie:
Skorzystam z:
[tex]\sqrt[n]{a}=a^\frac{1}{n}\\\\\sqrt[n]{a^m}=a^{\frac{m}{n}}\\\\a^n\cdot a^m=a^{n+m}\\\\a^n:a^m=a^{n-m}\\\\(a^n)^m=a^{n\cdot m}[/tex]
[tex]a)\\\sqrt3\cdot\sqrt[3]9\cdot\sqrt[5]{27}=\sqrt3\cdot\sqrt[3]{3^2}\cdot\sqrt[5]{3^3}=3^\frac{1}{2}\cdot3^\frac{2}{3}\cdot3^\frac{3}{5}=3^{\frac{1}{2}+\frac{2}{3}+\frac{3}{5}}=(*)\\\\\dfrac{1}{2}+\dfrac{2}{3}+\dfrac{3}{5}=\dfrac{1\cdot15}{2\cdot15}+\dfrac{2\cdot10}{3\cdot10}+\dfrac{3\cdot6}{5\cdot6}=\dfrac{15}{30}+\dfrac{20}{30}+\dfrac{18}{30}=\dfrac{53}{30}\\\\(*)=\huge\boxed{3^{\frac{53}{30}}}[/tex]
[tex]b)\\25^{\frac{3}{4}}:125^{-\frac{5}{2}}=\left(5^2\right)^{\frac{3}{4}}:\left(5^3\right)^{-\frac{5}{2}}=5^{2\cdot\frac{3}{4}}:5^{3\cdot\left(-\frac{5}{2}\right)}=5^{\frac{3}{2}}:5^{-\frac{15}{2}}=5^{\frac{3}{2}-\left(-\frac{15}{2}\right)}\\\\=5^{\frac{3}{2}+\frac{15}{2}}=5^{\frac{18}{2}}=\huge\boxed{5^9}[/tex]
