USA Olympiad Radical Simplification: solve for a=?

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Expand inside out: a^{1/2} → a^{3/2} → a^{3/4} → a^{7/4} → a^{7/8} = 3. Thus, a=3^{8/7}
Expand outside in: a√(a√a)=3^2 → a^3√a=3^4 → a^7=3^8. Thus, a=(3^8)^{1/7}=3^{8/7}