Hard Modulo arithmetic

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If I have $$c ≡ 169 \mod1643\\c=m^7\mod1643\\m=c^{951}\mod1643$$

How would I go about solving for m

I tried to write $$m^7 ≡169\mod1643$$

but I'm not sure what do do from here

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All you need is $m\equiv 169^{951} \pmod {1643}$. Feeding that to Alpha gives $1372$. Then $1372^7 \equiv 1335 \pmod {1643}$ so your equivalences are inconsistent.