Question

We all know unit digit of 9 is based on odd and even.
That means,
${9}^{1} = 9 \\ {9}^{2} = 1 \\ {9}^{3} = 9$
So on..
So if we take an example like
${29}^{733} = 9$
because 3 is an odd number answer will be 9.
One more example:
${49}^{2344} = 1$
because 4 is an even number answer will be 1.
Now for this example:
${29}^{612} = 9$
2 is an even number. The answer should be 1. why its 9?​

Answer 1

$\Large\textrm{ 29^{612} does not end with 9.}$

$\Large\textrm{We know that: -}$

$\textrm{Any digit except the unit digit does not affect the last digit.}$

$\textrm{Hence, ending digit is 9,1,9,1,\cdots .}$

$\Large\textrm{So let us consider again: -}$

$29^{612}\rightarrow9^{612}\rightarrow9^{2\times306}\rightarrow1$

$\textrm{Hence, 29^{612} ends with 1.}$