C. 3
Pembahasan:
[tex]\begin{aligned}\sf \frac{ {9}^{ - \frac{2}{3} } \: . \: {3}^{ - \frac{2}{3} } + {27}^{ - 1} }{ {27}^{ - \frac{4}{3} } + {81}^{ - \frac{3}{4} } } &=\sf \frac{ {( {3}^{2}) }^{ - \frac{2}{3} } \: . \: {3}^{ - \frac{2}{3} } + { {(3}^{3} )}^{ - 1} }{ { {(3}^{3} )}^{ - \frac{4}{3} } + { {(3}^{4} )}^{ - \frac{3}{4} } } \\ \\ \sf &=\sf \frac{ {3}^{ - \frac{4}{3} } \: . \: {3}^{ - \frac{2}{3} } + {3}^{ - 3} }{ {3}^{ - 4} + {3}^{ - 3} } \\ \\ \sf &= \sf \frac{ {3}^{ - 2} + \dfrac{1}{ {3}^{3} } }{ \dfrac{1}{ {3}^{4} } + \dfrac{1}{ {3}^{3} } } \\ \\ \sf &=\sf \dfrac{ \dfrac{1}{ {3}^{2} } + \dfrac{1}{ {3}^{3} } }{ \dfrac{1}{ {3}^{4} } + \dfrac{1}{ {3}^{3} } }\\ \\\sf &=\sf \dfrac{ \dfrac{1}{9 } + \dfrac{1}{ 27 } }{ \dfrac{1}{81 } + \dfrac{1}{ 27 } } \\ \\ \sf &=\sf \frac{ \dfrac{4}{27} }{ \dfrac{4}{81} } \\ \\\sf &=\sf \frac{ \cancel4}{27} \times \frac{81}{ \cancel4} \\ \\ \sf &=\sf3\end{aligned}[/tex]
Jadi, jawaban yang tepat adalah opsi (C).
