[tex]a)\\\\5^{\frac12}*5^{\frac14}=5^{\frac12+\frac14}=5^{\frac24+\frac14}=5^{\frac34}\\b)\\\\3^{\frac23}:3^{\frac16}=3^{\frac23-\frac16}=3^{\frac{4}{6}-\frac16}=3^{\frac36}=3^{\frac12}\\\\c) \\\\7^{\frac15}*7^{-\frac1{10}}=7^{\frac15+(-\frac1{10})}=7^{\frac{2}{10}-\frac1{10}}=7^{\frac1{10}}\\\\d) \\\\(6^{-\frac23})^{\frac15}=6^{-\frac23*\frac15}=6^{-\frac2{15}}[/tex]
[tex]e)\\\\5^{-\frac14}*5^{-\frac12}*5=5^{-\frac14-\frac12+1}=5^{-\frac14-\frac24+\frac44}=5^{-\frac34+\frac44}=5^{\frac14}\\\\f) \\\\3^{-\frac43}:3^{\frac16}*3^2=3^{-\frac43-\frac16+2}=3^{-\frac86-\frac16+2}=3^{-\frac96+\frac{12}6}=3^{\frac36}=3^{\frac12}\\\\g) \\\\(7^{\frac14})^2*7^{\frac34}=7^{\frac14*2+\frac34}=7^{\frac12+\frac34}=7^{\frac24+\frac34}=7^{\frac54}\\\\h)\\[/tex]
[tex]\\2^{-\frac15}:(2^{\frac25})^{-\frac14}=2^{-\frac15-\frac25*(-\frac14)}=2^{-\frac15+\frac2{20}}=2^{-\frac4{20}+\frac2{20}}=2^{-\frac2{20}}=2^{-\frac1{10}}[/tex]
[tex]i)\\2^{\frac23}*8^{\frac16}=2^{\frac23}*(2^3)^{\frac16}=2^{\frac23+3*\frac16}=2^{\frac23+\frac12}=2^{\frac{4}{6}+\frac36}=2^{\frac76}\\\\j)\\\\3^{-\frac14}*9^{\frac34}=3^{-\frac14}*(3^2)^{\frac34}=3^{-\frac14+2*\frac34}=3^{-\frac14+\frac32}=3^{-\frac14+\frac{6}{4}}=3^{\frac54}\\\\k)\\\\25^{\frac13}:5^{-\frac23}=(5^2)^{\frac13}:5^{-\frac23}=5^{\frac23-(-\frac23)}=5^{\frac23+\frac23}=5^{\frac43}[/tex]
[tex]l)\\4^{-\frac25}:2^{-\frac3{10}}=(2^2)^{-\frac25}:2^{-\frac3{10}}=2^{2*(-\frac25)-(-\frac3{10})}=2^{-\frac45+\frac3{10}}=2^{-\frac8{10}+\frac3{10}}=2^{-\frac5{10}}=2^{-\frac12}[/tex]
