거듭제곱근 대소 비교

[출제의도] 거듭제곱근 값의 대소 비교하기 $\displaystyle \mathrm{A} ^{12} = \left( \sqrt[3]{2} \right) ^{12} = \left( \sqrt[3]{2 ^{12}} \right) = 2 ^{\frac{12}{3}} = 16$ $\displaystyle \mathrm{B} ^{12} = \left( \sqrt[4]{3} \right) ^{12} = \left( \sqrt[4]{3 ^{12}} \right) = 3 ^{\frac{12}{4}} = 27$ $\displaystyle \mathrm{C} ^{12} = \left( \sqrt[6]{5} \right) ^{12} = \left( \sqrt[6]{5 ^{12}} \right) = 5 ^{\frac{12}{6}} = 25$ $\therefore$$\mathrm{A} < C < B$