EKSPONEN-ANEKA CONTOH SOAL LANJUTAN (BAGIAN 6)

$\begin{array}{ll}\\ 26.&\textrm{Nilai dari}\: \: \displaystyle \sqrt[4]{4}-\sqrt{2}=....\\ &\begin{array}{llll}\\ \textrm{a}.&-2\\ \textrm{b}.&-1\\ \textrm{c}.&0\\ \textrm{d}.&1\\ \textrm{e}.&2 \end{array}\\\\ &\textrm{Jawab}:\quad \textbf{c}\\ &\textrm{Perhatikan bahwa}\\ &\begin{aligned}&\displaystyle \sqrt[4]{4}-\sqrt{2}=\displaystyle \sqrt[2]{\sqrt[2]{2^{2}}}-\sqrt{2}=\sqrt{2}-\sqrt{2}=0 \end{aligned} \end{array}$.

$\begin{array}{ll}\\ 27.&\textrm{Nilai dari}\: \: \displaystyle \frac{\sqrt[\displaystyle 3]{64}}{\sqrt[\displaystyle 4]{64}}=....\\ &\begin{array}{llll}\\ \textrm{a}.&\displaystyle \frac{1}{2}\sqrt{2}\\ \textrm{b}.&\sqrt{2}\\ \textrm{c}.&2\sqrt{2}\\ \textrm{d}.&3\\ \textrm{e}.&4 \end{array}\\\\ &\textrm{Jawab}:\quad \textbf{b}\\ &\textrm{Perhatikan bahwa}\\ &\begin{aligned}&\displaystyle \frac{\sqrt[\displaystyle 3]{64}}{\sqrt[\displaystyle 4]{64}}=\displaystyle \frac{\sqrt[\displaystyle 3]{4^{\displaystyle 3}}}{\sqrt[\displaystyle 4]{8^{\displaystyle 2}}}=\displaystyle \frac{\sqrt[\displaystyle 3]{4^{\displaystyle 3}}}{\sqrt[\displaystyle 4]{\sqrt{8}^{\displaystyle 4}}}=\frac{4}{\sqrt{8}}\\ &=\frac{4}{\sqrt{8}}\times \frac{\sqrt{8}}{\sqrt{8}}=\frac{4}{8}\left( \sqrt{8} \right)\\ &=\frac{1}{2}\left( 2\sqrt{2} \right)=\sqrt{2} \end{aligned} \end{array}$.

$\begin{array}{ll}\\ 28.&\textrm{Nilai dari}\: \: \displaystyle \frac{\sqrt{\sqrt{25}}}{\sqrt{5}}=....\\ &\begin{array}{llll}\\ \textrm{a}.&5\\ \textrm{b}.&\sqrt{5}\\ \textrm{c}.&\displaystyle \frac{1}{2}\sqrt{5}\\ \textrm{d}.&1\\ \textrm{e}.&\displaystyle \frac{1}{2} \end{array}\\\\ &\textrm{Jawab}:\quad \textbf{d}\\ &\textrm{Perhatikan bahwa}\\ &\begin{aligned}&\displaystyle \frac{\sqrt{\sqrt{25}}}{\sqrt{5}}=\frac{\sqrt{\sqrt[\displaystyle 2]{5^{\displaystyle 2}}}}{\sqrt{5}}=\frac{\sqrt{5}}{\sqrt{5}}=1 \end{aligned} \end{array}$.

$\begin{array}{ll}\\ 29.&\textrm{Nilai dari}\: \: \displaystyle \frac{\sqrt{49\sqrt{7}}}{\sqrt{7\sqrt{49}}}=....\\ &\begin{array}{llll}\\ \textrm{a}.&7\\ \textrm{b}.&7\sqrt{7}\\ \textrm{c}.&\displaystyle \frac{1}{2}\sqrt{7}\\ \textrm{d}.&\sqrt{7}\\ \textrm{e}.&\displaystyle \sqrt[\displaystyle 4]{7} \end{array}\\\\ &\textrm{Jawab}:\quad \textbf{e}\\ &\textrm{Perhatikan bahwa}\\ &\begin{aligned}&\displaystyle \frac{\sqrt{49\sqrt{7}}}{\sqrt{7\sqrt{49}}}=\displaystyle \frac{7.\sqrt[\displaystyle 4]{7}}{\sqrt{7}.\sqrt[\displaystyle 4]{49}}=\displaystyle \frac{7.\sqrt[\displaystyle 4]{7}}{\sqrt{7}.\sqrt[\displaystyle 4]{7^{\displaystyle 2}}}\\ &=\displaystyle \frac{7.\sqrt[\displaystyle 4]{7}}{\sqrt{7}.\sqrt{7}}=\displaystyle \frac{7.\sqrt[\displaystyle 4]{7}}{7}=\sqrt[\displaystyle 4]{7} \end{aligned} \end{array}$.

 $\begin{array}{ll}\\ 30.&\textrm{Nilai dari}\: \: \displaystyle \left( \frac{1}{2} \right)^{\displaystyle \frac{1}{2}}-\left( \frac{1}{4} \right)^{\displaystyle \frac{1}{4}}=....\\ &\begin{array}{llll}\\ \textrm{a}.&-2\\ \textrm{b}.&-1\\ \textrm{c}.&0\\ \textrm{d}.&1\\ \textrm{e}.&2 \end{array}\\\\ &\textrm{Jawab}:\quad \textbf{c}\\ &\textrm{Perhatikan bahwa}\\ &\begin{aligned}&\displaystyle \left( \frac{1}{2} \right)^{4}=\left( \frac{1}{4} \right)^{2}\Leftrightarrow \displaystyle \left( \frac{1}{2} \right)^{\displaystyle \frac{4}{1}}=\left( \frac{1}{4} \right)^{\displaystyle \frac{2}{1}}\\ &\Leftrightarrow \left( \frac{1}{2} \right)^{\displaystyle \frac{1}{2}}=\left( \frac{1}{4} \right)^{\displaystyle \frac{1}{4}}\\ &\Leftrightarrow \left( \frac{1}{2} \right)^{\displaystyle \frac{1}{2}}-\left( \frac{1}{4} \right)^{\displaystyle \frac{1}{4}}=0 \end{aligned} \end{array}$.