Challenge:
If \(a^{x }= \frac{2}{3}\), what is the value of \(a^{-3x}\)?
A- \(\frac{2}{27}\)
B- \(-\frac{2}{27}\)
C- \(\frac{8}{27}\)
D- \(-\frac{8}{27}\)
E- \(-\frac{27}{8}\)
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The correct answer is E.
\(a^{x} = \frac{2}{3 }→ a^{-3x} = (\frac{2}{3})^{-3} = \frac{1}{(\frac{2}{3})^{3}} = \frac{1}{\frac{8}{27}} =\frac{ 27}{8}\)
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