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While performing some arithmetic operations, i am stuck at one point.I want to know is it possible to write ($a^b)\%p$ as ($a^{(b\%p)})\%p$?

rahul sharma
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    No, you need to use the properties given in the dupes. You can find easy counterexamples your claim, e.g. apply it to little Fermat $,a^p\equiv a\pmod{p}\ \ $ – Bill Dubuque Sep 13 '20 at 21:09

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The answer is no, and almost any randomly chosen set of values is a counterexample (for example, take $p=3$ and $a=2$ and $b=4$).

You're right to hope for some kind of reduction shortcut in the exponent. For that you should check out Fermat's little theorem and its generalization Euler's theorem.

Greg Martin
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