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SMK Teknologi dan Rekayasa

Solusi Paket 59 UN 2011 Matematika SMK Teknologi (8)


Nilai\ dari\ (216)^{\frac{1}{3}}+(\frac{1}{64})^{-\frac{1}{3}}-(27)^{\frac{1}{3}}\ adalah\ ....\\A.\ \ -4\\B.\ \ -1\\C.\ \ 6\\D.\ \ 7\\E.\ \ 13

Jawaban: D

Alternatif 1 (dengan menggunakan pangkat)

\begin{array}{rcl}(216)^{\frac{1}{3}}+(\frac{1}{64})^{-\frac{1}{3}}-(27)^{\frac{1}{3}}&=&(6^3)^{\frac{1}{3}}+(\frac{1}{4^3})^{-\frac{1}{3}}-(3^3)^{\frac{1}{3}}\\\\&=&6^{3\times {\frac{1}{3}}}+(4^{-3})^{-\frac{1}{3}}-3^{3\times {\frac{1}{3}}}\\\\&=&6^1+4^{-3\times (-\frac{1}{3})}-3^1\\\\&=&6+4^1-3\\\\&=&6+4-3\\\\&=&7\end{array}

Alternatif 2 (dengan menggunakan akar)

\begin{array}{rcl}(216)^{\frac{1}{3}}+(\frac{1}{64})^{-\frac{1}{3}}-(27)^{\frac{1}{3}}&=&\sqrt[3]{216}+\frac{1}{(\frac{1}{64})^{\frac{1}{3}}}-\sqrt[3]{27}\\\\&=&6+\frac{1}{\sqrt[3]{\frac{1}{64}}}-3\\\\&=&6+\frac{1}{\frac{1}{4}}-3\\\\&=&6+4-3\\\\&=&7\end{array}

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