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Problem Arrange the numbers 8 2 3 , 27 3 4 , 32 4 5 , 4 5 2 8^{\tfrac{2}{3}},\;27^{\tfrac{3}{4}},\;32^{\tfrac{4}{5}},\;4^{\tfrac{5}{2}} 8 3 2 , 2 7 4 3 , 3 2 5 4 , 4 2 5 in ascending order.
a) 27 3 4 , 8 2 3 , 32 4 5 , 4 5 2 27^{\tfrac{3}{4}},\;8^{\tfrac{2}{3}},\;32^{\tfrac{4}{5}},\;4^{\tfrac{5}{2}} 2 7 4 3 , 8 3 2 , 3 2 5 4 , 4 2 5
b) 8 2 3 , 4 5 2 , 27 3 4 , 32 4 5 8^{\tfrac{2}{3}},\;4^{\tfrac{5}{2}},\;27^{\tfrac{3}{4}},\;32^{\tfrac{4}{5}} 8 3 2 , 4 2 5 , 2 7 4 3 , 3 2 5 4
c) 8 2 3 , 27 3 4 , 32 4 5 , 4 5 2 8^{\tfrac{2}{3}},\;27^{\tfrac{3}{4}},\;32^{\tfrac{4}{5}},\;4^{\tfrac{5}{2}} 8 3 2 , 2 7 4 3 , 3 2 5 4 , 4 2 5
d) 8 2 3 , 32 4 5 , 27 3 4 , 4 5 2 8^{\tfrac{2}{3}},\;32^{\tfrac{4}{5}},\;27^{\tfrac{3}{4}},\;4^{\tfrac{5}{2}} 8 3 2 , 3 2 5 4 , 2 7 4 3 , 4 2 5
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