\((x+y)^{\frac{2}{3}}+(x-y)^{\frac{2}{3}}\)

Algebra Level 1

If \[a^{\frac{2}{3}}+b^{\frac{2}{3}}=16, x=a+3a^{\frac{1}{3}}b^{\frac{2}{3}}, y=b+3a^{\frac{2}{3}}b^{\frac{1}{3}},\] what is the value of \[(x+y)^{\frac{2}{3}}+(x-y)^{\frac{2}{3}}?\]

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