Prove by induction that an expression is divisible by 11

Keep going!

$64\cdot 2^{3k-1} + 45\cdot 3^k = 9(2^{3k-1} + 5\cdot3^k) + 55\cdot2^{3k-1}$

hint: You may want to reconsider the way you split the terms at the end.

Note that $64(2^{3k - 1}) + 45(3^k) = 9(2^{3k - 1} + 5(3^k)) + 55(2^{3k - 1})$