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[tex]\begin{cases}a\equiv1\pmod7\\b\equiv2\pmod7\\c\equiv6\pmod7\end{cases}[/tex]

[tex]a^{81}\equiv1^{81}\equiv1\pmod7[/tex]

[tex]b^{91}\equiv2^{91}\pmod7[/tex]

[tex]2^{91}\equiv(2^3)^{30}\times2^1\equiv8^{30}\times2\pmod7[/tex]
[tex]8\equiv1\pmod7[/tex]
[tex]2\equiv2\pmod7[/tex]
[tex]\implies2^{91}\equiv1^{30}\times2\equiv2\pmod7[/tex]

[tex]c^{27}\equiv6^{27}\pmod7[/tex]

[tex]6^{27}\equiv(-1)^{27}\equiv-1\equiv6\pmod7[/tex]

[tex]\implies a^{81}b^{91}c^{27}\equiv1\times2\times6\equiv12\equiv5\pmod7[/tex]

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