EKSPONEN-ANEKA CONTOH SOAL LANJUTAN (BAGIAN 7)

 $\begin{array}{ll}\\ 31.&\textrm{Nilai dari}\: \: \displaystyle \frac{-1^{\displaystyle 0}+1^{\displaystyle 0}-2^{\displaystyle 0}+2^{\displaystyle 0}}{(-1)^{\displaystyle 0}+1^{\displaystyle 0}}=....\\ &\begin{array}{llll}\\ \textrm{a}.&-2\\ \textrm{b}.&-1\\ \textrm{c}.&0\\ \textrm{d}.&1\\ \textrm{e}.&2 \end{array}\\\\ &\textrm{Jawab}:\quad \textbf{c}\\ &\textrm{Perhatikan bahwa}\\ &\begin{aligned}&\displaystyle \frac{-1^{\displaystyle 0}+1^{\displaystyle 0}-2^{\displaystyle 0}+2^{\displaystyle 0}}{(-1)^{\displaystyle 0}+1^{\displaystyle 0}}\\ &=\displaystyle \frac{-1+1-1+1}{1+1}=\frac{0}{2}=0  \end{aligned}  \end{array}$.

$\begin{array}{ll}\\ 32.&\textrm{Nilai dari}\: \: \displaystyle 2^{\displaystyle 2^{\displaystyle 2^{\displaystyle 2^{\displaystyle 0}}}}-\displaystyle 2^{\displaystyle 2^{\displaystyle 2^{\displaystyle 0^{\displaystyle 2}}}}-\displaystyle 2^{\displaystyle 2^{\displaystyle 0^{\displaystyle 2^{\displaystyle 2}}}}=....\\ &\begin{array}{llll}\\ \textrm{a}.&4\\ \textrm{b}.&6\\ \textrm{c}.&8\\ \textrm{d}.&10\\ \textrm{e}.&12 \end{array}\\\\ &\textrm{Jawab}:\quad \textbf{d}\\ &\textrm{Perhatikan bahwa}\\ &\begin{aligned}&\displaystyle 2^{\displaystyle 2^{\displaystyle 2^{\displaystyle 2^{\displaystyle 0}}}}=\displaystyle 2^{\displaystyle 2^{\displaystyle 2^{\displaystyle 1}}}=\displaystyle 2^{\displaystyle 2^{\displaystyle 2}}=\displaystyle 2^{\displaystyle 4}=16\\ &\textrm{Sedangkan untuk}\\ &\displaystyle 2^{\displaystyle 2^{\displaystyle 2^{\displaystyle 0^{\displaystyle 2}}}}=\displaystyle 2^{\displaystyle 2^{\displaystyle 2^{\displaystyle 0}}}=\displaystyle 2^{\displaystyle 2^{\displaystyle 1}}=\displaystyle 2^{\displaystyle 2}=4\\ &\textrm{Selanjutnya untuk}\\ &\displaystyle 2^{\displaystyle 2^{\displaystyle 0^{\displaystyle 2^{\displaystyle 2}}}}=\displaystyle 2^{\displaystyle 2^{\displaystyle 0^{\displaystyle 4}}}=\displaystyle 2^{\displaystyle 2^{\displaystyle 0}}=2^{\displaystyle 1}=2\\ &\textrm{Sehingga}\\ &\displaystyle 2^{\displaystyle 2^{\displaystyle 2^{\displaystyle 2^{\displaystyle 0}}}}-\displaystyle 2^{\displaystyle 2^{\displaystyle 2^{\displaystyle 0^{\displaystyle 2}}}}-\displaystyle 2^{\displaystyle 2^{\displaystyle 0^{\displaystyle 2^{\displaystyle 2}}}}=16-4-2=10 \end{aligned}  \end{array}$.

$\begin{array}{ll}\\ 33.&\textrm{Nilai dari}\: \: \displaystyle x\displaystyle ^{\displaystyle x}=256,\quad \textrm{maka nilai}\quad x^{\displaystyle 2}-2^{\displaystyle x}=....\\ &\begin{array}{llll}\\ \textrm{a}.&-4\\ \textrm{b}.&-1\\ \textrm{c}.&0\\ \textrm{d}.&1\\ \textrm{e}.&4 \end{array}\\\\ &\textrm{Jawab}:\quad \textbf{c}\\ &\textrm{Diketahui bahwa}\\ &\begin{aligned}&\displaystyle x\displaystyle ^{\displaystyle x}=256= 16^{\displaystyle 2}=\left( 4 ^{\displaystyle 2} \right)^{\displaystyle 2}=4^{\displaystyle 4}\Leftrightarrow x=4\\ &\textrm{Sehingga untuk}\\ &x^{\displaystyle 2}-2^{\displaystyle x}=4^{\displaystyle 2}-2^{\displaystyle 4}=16-16=0  \end{aligned} \end{array}$.

$\begin{array}{ll}\\ 34.&\textrm{Nilai dari}\quad \displaystyle \frac{2^{\displaystyle 2^{\displaystyle n}+2^{\displaystyle n+1}}}{2^{\displaystyle 3.2^{\displaystyle n}}}\quad \textrm{adalah}\:....\\ &\begin{array}{llll}\\ \textrm{a}.&\displaystyle \frac{1}{8}\\ \textrm{b}.&\displaystyle \frac{1}{4}\\ \textrm{c}.&\displaystyle \frac{1}{2}\\ \textrm{d}.&1\\ \textrm{e}.&2 \end{array}\\\\ &\textrm{Jawab}:\quad \textbf{d}\\ &\textrm{Diketahui bahwa}\\ &\begin{aligned}&\displaystyle \frac{2^{\displaystyle 2^{\displaystyle n}+2^{\displaystyle n+1}}}{2^{\displaystyle 3.2^{\displaystyle n}}}=\displaystyle \frac{2^{\displaystyle 2^{\displaystyle n}+2^{\displaystyle n}.2^{\displaystyle 1}}}{2^{\displaystyle 3.2^{\displaystyle n}}}\\ &=\displaystyle \frac{2^{\displaystyle 2^{\displaystyle n}+2.2^{\displaystyle n}}}{2^{\displaystyle 3.2^{\displaystyle n}}}=\displaystyle \frac{2^{\displaystyle (1+2).2^{\displaystyle n}}}{2^{\displaystyle 3.2^{\displaystyle n}}}\\ &=\displaystyle \frac{2^{\displaystyle 3.2^{\displaystyle n}}}{2^{\displaystyle 3.2^{\displaystyle n}}}=1 \end{aligned} \end{array}$.

$\begin{array}{ll}\\ 35.&\textrm{Nilai dari}\: \: \displaystyle \left( \frac{1}{64} \right)^{\displaystyle -9^{\displaystyle -2^{\displaystyle -1}}}=....\\ &\begin{array}{llll}\\ \textrm{a}.&1\\ \textrm{b}.&4\\ \textrm{c}.&\displaystyle \frac{1}{4}\\ \textrm{d}.&-\displaystyle \frac{1}{4}\\ \textrm{e}.&-4 \end{array}\\\\ &\textrm{Jawab}:\quad \textbf{b}\\ &\textrm{Perhatikan bahwa}\\ &\begin{aligned}&\displaystyle \left( \frac{1}{64} \right)^{\displaystyle -9^{\displaystyle -2^{\displaystyle -1}}}=\displaystyle \left( \frac{1}{64} \right)^{\displaystyle -9^{\displaystyle -\frac{1}{2}}}\\ &=\displaystyle \left( \frac{1}{64} \right)^{\displaystyle -\left( \displaystyle \frac{1}{9} \right)^{\displaystyle \frac{1}{2}}}=\displaystyle \left( \frac{1}{64} \right)^{\displaystyle -\sqrt{\displaystyle \frac{1}{9}}}\\ &=\displaystyle \left( \frac{1}{64} \right)^{\displaystyle -\frac{1}{3}}=64^{\displaystyle \frac{1}{3}}=\left( 4^{\displaystyle 3} \right)^{\displaystyle \frac{1}{3}}=4^{\displaystyle \frac{3}{3}}=4  \end{aligned}  \end{array}$.