[tex]a)\\\\ \frac{5^ {\frac{1}{4}}* \sqrt{125} *25^{\frac{5}{8}} }{\sqrt[4]{5} *\sqrt[8]{25} }= \frac{5^ {\frac{1}{4}}* 125^{\frac{1}{2}} * (5^2)^{\frac{5}{8}} }{5^{\frac{1}{4}} *25^{\frac{1}{8}}}= \frac{5^ {\frac{1}{4}}* (5^3)^{\frac{1}{2}} * (5^2)^{\frac{5}{8}} }{5^{\frac{1}{4}} * (5^2)^{\frac{1}{8}}}= \frac{5^ {\frac{1}{4}}* 5 ^{\frac{3}{2}} * 5 ^{\frac{5}{4}} }{5^{\frac{1}{4}} * 5 ^{\frac{1}{4}}} =[/tex]
[tex]= \frac{5^ {\frac{1}{4}+\frac{3}{2}+\frac{5}{4}} }{5^{\frac{1}{4}+\frac{1}{4}}} = \frac{5^ {\frac{6}{4}+\frac{3}{2} } }{5^{\frac{2}{4} }} = \frac{5^ {\frac{3}{2}+\frac{3}{2} } }{5^{\frac{1}{2} }} = \frac{5^ {\frac{6}{2} } }{5^{\frac{1}{2} }} =5 ^{\frac{6}{2}-\frac{1}{2}} =5^{\frac{5}{2}} \\\\b)\\\\5^{\frac{5}{2} }=\sqrt{5^5}=\sqrt{3125}[/tex]
