Evaluate:
[5(813+2713)3]14\Big[5\Big(8^{\dfrac{1}{3}}+ 27^{\dfrac{1}{3}}\Big)^3\Big]^{\dfrac{1}{4}}[5(831+2731)3]41
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[5(813+2713)3]14=[5((23)13+(33)13)3]14=[5((2)33+(3)33)3]14=[5(2+3)3]14=[5(5)3]14=(54)14=544=5\Big[5\Big(8^{\dfrac{1}{3}}+ 27^{\dfrac{1}{3}}\Big)^3\Big]^{\dfrac{1}{4}}\\[1em] = \Big[5\Big((2^3)^{\dfrac{1}{3}}+ (3^3)^{\dfrac{1}{3}}\Big)^3\Big]^{\dfrac{1}{4}}\\[1em] = \Big[5\Big((2)^{\dfrac{3}{3}}+ (3)^{\dfrac{3}{3}}\Big)^3\Big]^{\dfrac{1}{4}}\\[1em] = \Big[5(2 + 3)^3\Big]^{\dfrac{1}{4}}\\[1em] = \Big[5(5)^3\Big]^{\dfrac{1}{4}}\\[1em] = (5^4)^{\dfrac{1}{4}}\\[1em] = 5^{\dfrac{4}{4}}\\[1em] = 5[5(831+2731)3]41=[5((23)31+(33)31)3]41=[5((2)33+(3)33)3]41=[5(2+3)3]41=[5(5)3]41=(54)41=544=5
Hence, [5(813+2713)3]14=5\Big[5\Big(8^{\dfrac{1}{3}}+ 27^{\dfrac{1}{3}}\Big)^3\Big]^{\dfrac{1}{4}} = 5[5(831+2731)3]41=5.
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