26) x^{\sqrt[3]{x^2}} = (√x)^x

x^{\sqrt[3]{x^2}} = (√x)^x x^{\sqrt[3]{x^2}} = (x^{1/2})^x x^{\sqrt[3]{x^2}} = x^{x/2} Приравниваем показатели: \sqrt[3]{x^2} = x/2 (x^2)^(1/3) = x/2 x^(2/3) = x/2 x^(2/3) / x = 1/2 x^(2/3 - 1) = 1/2 x^(-1/3) = 1/2 1 / x^(1/3) = 1/2 x^(1/3) = 2 (x^(1/3))^3 = 2^3 x = 8 Проверим: 8^(√[3]{8^2}) = (√8)^8 8^(√[3]{64}) = (√8)^8 8^4 = (√8)^8 (2^3)^4 = (2^(3/2))^8 2^12 = 2^12 верно Также надо рассмотреть случай x = 1 1^(√[3]{1^2}) = (√1)^1 1 = 1 верно Ответ: x = 1, x = 8