Take out some values of \(3\) when raised to the power

\(3^1 = 3\) when divided by \(8\) remainder \(= 3\)

\(3^2 = 9\) when divided by \(8\) remainder \(= 1\)

\(3^3 = 27\) when divided by \(8\) remainder \(= 3\)

\(3^4 = 81\) when divided by \(8\) remainder \(= 1\)

There is a continuous pattern of \(3\) and \(1\) repeating when \(3\) is raised to a power of something and is divided by\(8\)

Hence the possible ans choices are \(3\) and \(1\) however, \(3\) is the ans when \(3\) is raised to odd powers and \(1\) is the ans when \(3\) is raised to even power

therefore, option c

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This is my response to the question and may be incorrect. Feel free to rectify any mistakes