a)
[tex]9^{\frac{5}{6} } *9^{\frac{2}{3} }=9^{\frac{3}{2} }=(3^{2} )^{\frac{3}{2} } =3^{3} =27[/tex]
b)
[tex]8^{\frac{4}{5} } :8^{\frac{2}{15} } =8^{\frac{2}{3} } =(2^{3})^{\frac{2}{3} } =2^{2}=4[/tex]
c)
[tex](\frac{2}{5} )^{-\frac{1}{2} } *(\frac{5}{18} )^{-\frac{1}{2} } =(\frac{2}{5}*\frac{5}{18} )^{-\frac{1}{2} }=(\frac{1}{9} )^{-\frac{1}{2} } =9^{\frac{1}{2} } =\sqrt{9}=3[/tex]
d)
[tex](2\frac{2}{3}) ^{1\frac{1}{2} } :(\frac{2}{3} )^{1\frac{1}{2} }=(\frac{8}{3}:\frac{2}{3}) ^\frac{3}{2} } =(\frac{8}{3} *\frac{3}{2} )^{\frac{3}{2} } =(\frac{4}{1} )^{\frac{3}{2} } =(2^{2} )^{\frac{3}{2} }=2^{3}=8[/tex]
e)
[tex]((\frac{4}{9} )^{\frac{3}{4} } )^{-\frac{2}{3} } =(\frac{4}{9} )^{-\frac{1}{2} } =(\frac{9}{4} )^{\frac{1}{2} }=\sqrt{\frac{9}{4} } =\frac{3}{2} =1\frac{1}{2}[/tex]
