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27^1/3 = 3
therefore [5(8^1/3 + 27^1/3)^3]^1/4 = [5(2+3)^3]^1/4
= [5(5)^3]^1/4
now we know that a^m x a^n = a^m+n
so [5(5^3)]^1/4 = (5^1+3)^1/4 = (5^4)^1/4 = 5
hence the answer is 5
(5*(2+3) power 3) to the power 1/4
(5*5raised 3) whole raised to 1/4
(5 raised to 4) raised to 1/4
=5