EKSPONEN-ANEKA CONTOH SOAL LANJUTAN (BAGIAN 8)

 $\begin{array}{ll}\\ 36.&\textrm{Nilai dari}\: \: x^{\displaystyle 6}\quad \textrm{pada}\quad x^{\displaystyle x^{\displaystyle 6}}=\sqrt[\displaystyle 12]{\displaystyle \frac{1}{2}}\quad \textrm{adalah}\:....\\ &\begin{array}{llll}\\ \textrm{a}.&2\\ \textrm{b}.&\displaystyle \frac{1}{4}\\ \textrm{c}.&\displaystyle \frac{1}{2}\\ \textrm{d}.&-\displaystyle \frac{1}{2}\\ \textrm{e}.&-2 \end{array}\\\\ &\textrm{Jawab}:\quad \textbf{c}\\ &\textrm{Diketahui bahwa}\quad x^{\displaystyle x^{\displaystyle 6}}=\sqrt[\displaystyle 12]{\displaystyle \frac{1}{2}}\:=\left( \displaystyle \frac{1}{2} \right)^{\displaystyle \frac{1}{12}}.\\ &\textrm{Perhatikan bahwa dengan memangkatkan 6}\\ &\textrm{di masing-masing ruas kita akan mendapatkan}\\ &\begin{aligned}&\left( x^{\displaystyle x^{\displaystyle 6}} \right)^{\displaystyle 6}=\left( \left( \displaystyle \frac{1}{2} \right)^{\displaystyle \frac{1}{12}} \right)^{\displaystyle 6}\\ &\Leftrightarrow x^{\displaystyle 6.x^{\displaystyle 6}}=\left( \displaystyle \frac{1}{2} \right)^{\left( \displaystyle \frac{1}{2} \right)}\\ &\Leftrightarrow \left( x^{\displaystyle 6} \right)^{\displaystyle x^{\displaystyle 6}}=\left( \displaystyle \frac{1}{2} \right)^{\left( \displaystyle \frac{1}{2} \right)}\\ &\Leftrightarrow x^{\displaystyle 6}=\displaystyle \frac{1}{2}  \end{aligned} \end{array}$.