GMAT Problem Solving (PS) | If X/Y=63^33×36^195, what is the remainder of X/(10Y)?

Its basically asking the remainder of\(\frac{63^{33}×36^{195}}{10}\)
And it all depends on the unit's digit of\(63^{33}×36^{195}\)

Units digit of\(63^{33}\) depends on cyclicity of 3.
\(63^{1}\) =3
\(63^{2}\) =9
\(63^{3}\) =7
\(63^{4}\) =1
\(63^{5}\) = 3
.
.
.
\(63^{32}\) = 1
\(63^{33}\) = 3

Hence the units digit would be:3

On the other hand, the units digit of\(36^{195}\) , will depend on cyclicity of 6, which is 1 and the units digit it always 6.

Hence the unit's digit of the expression\(63^{33}×36^{195}\) is\(3x6=18\) =>8

Therefore,
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