[tex]\it 1) \ \ =5^{\frac{1}{2}}\cdot5^{\frac{2}{3}}\cdot5^{-\frac{3}{5}}\cdot5^{-1}=5^{\frac{1}{2}+\frac{2}{3}-\frac{3}{5}-1}=5^{-\frac{13}{30}}\\ \\ \\ 2)\ \ =\dfrac{1}{2}log_5100- \dfrac{log_54}{log_5 25}=\dfrac{1}{2}log_5100- \dfrac{log_54}{2}=\dfrac{log_5 100-log_5 4}{2}=\\ \\ \\ =\dfrac{log_5\dfrac{100}{4}}{2}=\dfrac{log_525}{2}=\dfrac{2}{2}=1[/tex]
