Ich gehe mal davon aus, dass a > 0 und b > 0
(24^{1/3} + 2·81^{1/3} - 3·192^{1/3}) : 3^{1/3}
= 24^{1/3}/3^{1/3} + 2·81^{1/3}/3^{1/3} - 3·192^{1/3}/3^{1/3}
= 8^{1/3} + 2·27^{1/3} - 3·64^{1/3}
= 2 + 2·3 - 3·4
= 2 + 6 - 12
= -4
(a·b^2·(a^3·b)^{1/5} - (a·b^2)^{1/5}·a^3·b) : (a·b)^{7/5}
= a·b^2·(a^3·b)^{1/5}/(a·b)^{7/5} - (a·b^2)^{1/5}·a^3·b/(a·b)^{7/5}
= a·b^2·(a^3·b)^{1/5}·(a·b)^{-7/5} - (a·b^2)^{1/5}·a^3·b·(a·b)^{-7/5}
= a·b^2·a^{3/5}·b^{1/5}·a^{-7/5}·b^{-7/5} - a^{1/5}·b^{2/5}·a^3·b·a^{-7/5}·b^{-7/5}
= a^{1/5}·b^{4/5} - a^{9/5}
(2·a^4·b^2)^{1/3}·(4·a^8·b^7)^{1/3}
= 2^{1/3}·a^{4/3}·b^{2/3}·4^{1/3}·a^{8/3}·b^{7/3}
= 2^{1/3}·a^{4/3}·b^{2/3}·2^{2/3}·a^{8/3}·b^{7/3}
= 2^{3/3}·a^{12/3}·b^{9/3}
= 2^1·a^4·b^3
= 2·a^4·b^3