Question

100^1/3 * 2^8/6 * 1/5^5/3

Answer 1

100^1/3 * 2^8/6 * 1/5^5/3 = (5^2*2^2)^(1/3) *2^(4/3)*5(-5/3) = 5^(2/3)*2^(2/3)*2^(4/3)*5(-5/3) = 

=5^(2/3-5/3)*2^(2/3+4/3) = 5^(-3/3)*2^(6/3) =5^(-1)*2^2 =4/5 =0,8

 

 

Answer 2

$100^{frac{1}{3}} cdot 2^{frac{8}{6}} cdot frac{1}{5^{frac{5}{3}}}= 5^{2 cdot frac{1}{3}} cdot 2^{2 cdot frac{1}{3}} cdot 2^{frac{4}{3}} cdot 5^{- frac{5}{3}}} = \ = 5^{frac{2}{3}} cdot 2^{frac{2}{3}} cdot 2^{frac{4}{3}} cdot 5^{- frac{5}{3}} =5^{frac{2}{3} - frac{5}{3}} cdot 2^{frac{2}{3}+frac{4}{3}} = 5^{-frac{3}{3}} cdot 2^{frac{6}{3}} = \ =5^{-1} cdot 2^{2} = frac{4}{5} =0,8$