If \(a^2+\frac{1}{9^2}=\frac{7}{3}\), then what is the value of \(\left(a^3-\frac{1}{a^3}\right)\)?
As printed on the source sheet in both languages, the given relation is \(a^2+\frac{1}{9^2}=\frac{7}{3}\), which reads like a printing anomaly for the more standard identity-type relation \(a^2+\frac{1}{a^2}=\frac{7}{3}\). With the equation as printed literally, the reciprocal term is a fixed constant rather than depending on a, which does not connect cleanly to \(a^3-\frac{1}{a^3}\), so an independent numeric check could not be completed with confidence. The handwritten mark on the source sheet selects \(\frac{7}{\sqrt[3]{3}}\) (option A), which is transcribed here as the recorded choice.
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