\(\Rightarrow \frac{1}{3}=e^{-\lambda \times 3}=e^{-3 \lambda}\)   .........\((1)\)

Let activity in \(9\) days be \(R'\). Then

\(\frac{R^{\prime}}{R_{0}}=e^{-\lambda \times 9}=e^{-9 \lambda} e^{-\lambda \times 3}=\left(e^{-3 \lambda}\right)^{3}\)

\(=\left(\frac{1}{3}\right)^{3}, \quad\)    from \((1)\)

\(=\frac{1}{27} \Rightarrow R^{\prime}=\frac{R_{0}}{27}.\)