Find $r\equiv 9^{137}*x^{51}+36^{1003}(\mod 7)$

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For $x\equiv 1\mod 7$

I know that I can do $36^{1003}\equiv 1\mod 7$, but I do not understand how to go about the other part.

Thank you for any help.

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Hint: $9^3\equiv1\mod7$ and $36\equiv1\mod7$.