$\begin{array}{ll}\\ 6.&\textrm{Bentuk sederhana dari}\: \: \: \\ &\left (\displaystyle \frac{1}{2} \right )^{-\left ( \frac{1}{2} \right )^{-1}}+\left (\displaystyle \frac{1}{3} \right )^{-\left ( \frac{1}{3} \right )^{-1}}+\left (\displaystyle \frac{1}{4} \right )^{-\left ( \frac{1}{4} \right )^{-1}}+\left (\displaystyle \frac{1}{5} \right )^{-\left ( \frac{1}{5} \right )^{-1}}\\ &\textrm{adalah ... .}\\ &\begin{array}{llll}\\ \textrm{a}.&3142\\ \textrm{b}.&287\\ \color{red}\textrm{c}.&3412\\ \textrm{d}.&4116\\ \textrm{e}.&4096 \end{array}\\\\ &\textrm{Jawab}:\quad \color{red}\textbf{c}\\ &\color{blue}\begin{aligned}&\left (\displaystyle \frac{1}{2} \right )^{-\left ( \frac{1}{2} \right )^{-1}}+\left (\displaystyle \frac{1}{3} \right )^{-\left ( \frac{1}{3} \right )^{-1}}+\left (\displaystyle \frac{1}{4} \right )^{-\left ( \frac{1}{4} \right )^{-1}}+\left (\displaystyle \frac{1}{5} \right )^{-\left ( \frac{1}{5} \right )^{-1}}\\ &=\left (\displaystyle \frac{1}{2} \right )^{-2}+\left (\displaystyle \frac{1}{3} \right )^{-3}+\left (\displaystyle \frac{1}{4} \right )^{-4}+\left (\displaystyle \frac{1}{5} \right )^{-5}\\ &=2^{2}+3^{3}+4^{4}+5^{5}\\ &=4+27+256+3125\\ &=\color{red}3412 \end{aligned}\\ \end{array}$.
$\begin{array}{ll}\\ 7.&\textrm{Nilai dari}\\ &\underset{89}{\underbrace{(-7)(-7)(-7)\cdots (-7)}}-(-7)^{89}\\ &\textrm{adalah ... .}\\ &\begin{array}{llll}\\ \textrm{a}.&2\\ \textrm{b}.&7\\ \textrm{c}.&4\\ \color{red}\textrm{d}.&0\\ \textrm{e}.&9 \end{array}\\\\ &\textrm{Jawab}:\quad \color{red}\textbf{d}\\ &\color{blue}\begin{aligned}&\underset{89}{\underbrace{(-7)(-7)(-7)\cdots (-7)}}-(-7)^{89}\\ &=(-7)^{89}-(-7)^{89}\\ &=\color{red}0 \end{aligned}\\ \end{array}$.
$\begin{array}{ll}\\ 8.&\textrm{Nilai dari}\: \: \left ( \sqrt{3\times \sqrt[4]{27\times \sqrt[3]{81}}} \right )^{\displaystyle \frac{24}{25}}\\ &\textrm{adalah ... .}\\ &\begin{array}{llll}\\ \textrm{a}.&1\\ \textrm{b}.&2\\ \color{red}\textrm{c}.&3\\ \textrm{d}.&4\\ \textrm{e}.&5 \end{array}\\\\ &\textrm{Jawab}:\quad \color{red}\textbf{c}\\ &\color{blue}\begin{aligned}& \left ( \sqrt{3\times \sqrt[4]{27\times \sqrt[3]{81}}} \right )^{\displaystyle \frac{24}{25}}\\ &=\left ( 3^{\frac{1}{2}}.(3^{3})^{\frac{1}{2.4}}.(3^{4})^{\frac{1}{2.4.3}} \right )^{\displaystyle \frac{24}{25}}\\ &=\left ( 3^{\frac{1}{2}+\frac{3}{8}+\frac{4}{24}} \right )^{\displaystyle \frac{24}{25}}\\ &=3^{\frac{12}{25}+\frac{9}{25}+\frac{4}{25}}\\ &=3^{\frac{25}{25}}\\ &=\color{red}3 \end{aligned}\\ \end{array}$.
$\begin{array}{ll}\\ 9.&\textrm{Jika}\: \: \sqrt{27^{2x+3}}=\displaystyle \frac{1}{3^{x-2}.9^{3x}}\: ,\: \: \textrm{maka nilai}\\ &8x+2\: \: \textrm{adalah ... .}\\ &\begin{array}{llll}\\ \color{red}\textrm{a}.&0\\ \textrm{b}.&2\\ \textrm{c}.&4\\ \textrm{d}.&8\\ \textrm{e}.&12 \end{array}\\\\ &\textrm{Jawab}:\quad \color{red}\textbf{a}\\ &\textbf{Alternatif 1}\\ &\color{blue}\begin{aligned}\sqrt{27^{2x+3}}&=\displaystyle \frac{1}{3^{x-2}.9^{3x}}\\ 27^{\displaystyle \frac{2x+3}{2}}&=3^{-(x-2)}.9^{-3x}\\ 3^{3.\left ( \displaystyle \frac{2x+3}{2} \right )}&=3^{2-x}.3^{2(-3x)}\\ 3^{3.\left ( \displaystyle \frac{2x+3}{2} \right )}&=3^{2-x-6x}\\ \color{red}3\color{black}^{3.\left ( \displaystyle \frac{2x+3}{2} \right )}&=\color{red}3\color{black}^{2-7x}\\ \color{black}3\frac{(2x+3)}{2}&=\color{black}2-7x\\ 6x+9&=4-14x\\ 6x+14x&=4-9\\ 20x&=-5\\ &x=-\displaystyle \frac{1}{4}\\ \textrm{maka nilai}&\\ 8x+2&=8\left ( -\displaystyle \frac{1}{4} \right )+2=-2+2=\color{red}0 \end{aligned}\\ &\textbf{Alternatif 2}\\ &\color{blue}\begin{aligned}\sqrt{27^{2x+3}}&=\displaystyle \frac{1}{3^{x-2}.9^{3x}}\\ 27^{\displaystyle \frac{2x+3}{2}}.3^{x-2}.9^{3x}&=1\\ 3^{3\left ( \displaystyle \frac{2x+3}{2} \right )}.3^{x-2}.3^{2(3x)}&=3^{0}\\ 3^{3\left ( \displaystyle \frac{2x+3}{2} \right )+x-2+6x}&=3^{0}\\ \displaystyle \frac{3(2x+3)}{2}+7x-2&=0\\ 6x+9+14x-4&=0\\ 20x+5&=0\\ 20x&=-5\\ x&=-\displaystyle \frac{1}{4}\\ \textrm{Selanjutnya sama}&\\ \textrm{dengan langkah no.1}&\: \: \textrm{di atas} \end{aligned}\\ \end{array}$.
$\begin{array}{ll}\\ 10.&\textrm{Penyelesaian persamaan}\: \: 3^{2x+1}=81^{x-2}\: \\ &\textrm{adalah ... .}\\ &\begin{array}{llll}\\ \textrm{a}.&0\\ \textrm{b}.&2\\ \textrm{c}.&4\\ \color{red}\textrm{d}.&4\displaystyle \frac{1}{2}\\ \textrm{e}.&16 \end{array}\\\\ &\textrm{Jawab}:\quad \color{red}\textbf{d}\\ &\color{blue}\begin{aligned}3^{2x+1}&=81^{x-2}\\ 3^{2x+1}&=(3^{4})^{x-2}\\ 3^{2x+1}&=3^{4x-8}\\ \color{black}2x+1&=\color{black}4x-8\\ \color{black}2x-4x&=\color{black}-8-1\\ -2x&=-9\\ x&=\displaystyle \frac{-9}{-2}\\ &=\color{red}4\displaystyle \frac{1}{2} \end{aligned}\\ \end{array}$.
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