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A Nice Radical Equation Math Olympiad: ¹⁸√x = ˣ√3; x = ?(¹⁸√x)¹⁸ˣ = (ˣ√3)¹⁸ˣ, xˣ = 3¹⁸ = (3²)⁹ = 9⁹; x = 9Answer check:¹⁸√x = ¹⁸√9 = 3²⸍¹⁸ = ⁹√3 = ˣ√3; ConfirmedFinal answer:x = 9
A Nice Radical Equation Math Olympiad: ¹⁸√x = ˣ√3; x = ?
(¹⁸√x)¹⁸ˣ = (ˣ√3)¹⁸ˣ, xˣ = 3¹⁸ = (3²)⁹ = 9⁹; x = 9
Answer check:
¹⁸√x = ¹⁸√9 = 3²⸍¹⁸ = ⁹√3 = ˣ√3; Confirmed
Final answer:
x = 9