거듭제곱근 연산 보기

$\displaystyle R ( a , b ) = ^{a} \sqrt{b}$ ㄱ. $\displaystyle R ( 16 , 4 ) = ^{16} \sqrt{4} = ^{8} \sqrt{2} = R ( 8 , 2 )$ $\therefore$ 참 ㄴ. $R ( a , 5 ) \cdot R ( b , 5 )$ $\displaystyle = ^{a} \sqrt{5} ^{b} \sqrt{5}$ $\displaystyle = ^{\frac{ab}{a + b}} \sqrt{5} = R \left( \frac{ab}{a + b} , 5 \right) \ne R ( a + b , 5 )$ $\displaystyle \left( \because ( 5 ^{\frac{1}{a}} ) ( 5 ^{\frac{1}{b}} ) = 5 ^{\frac{1}{a} + \frac{1}{b}} = 5 ^{\frac{a + b}{ab}} \right)$ $\therefore$ 거짓 ㄷ. $\displaystyle R ( a , b ) = ^{a} \sqrt{b} = k$에서 $b = k ^{a}$ $a = \log _{k} b$ $\therefore$ 참 따라서, 옳은 것은 ㄱ, ㄷ이다.