Exponent of 3

\[\begin{array} {l l l } 3^3 = 27, & 2 + 7 &= 9 \\ 3^4 = 81, & 8 + 1 &= 9 \\ 3^{10} = 59049, & 5 + 9 + 0 + 4 + 9 &= 27 \\ 3^{15} = 14348907, & 1 + 4 + 3 + 4 + 8 + 9 + 0 + 7& = 36 \end{array} \]

True or False?

For any positive integer \(k>1\), the sum of digits of the representation of \(3^k\) is always divisible by 9.

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