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I want to decode $13^3$ (mod 34) but I have

$13^3 \equiv 13^2*13 \equiv (-1)^2 *13$ (mod 34)

and I'm stuck the answer is 21

I know I can $13^3 \equiv $ (mod 34) so $13^3=2197$
$13^3/34=2197/34=64$

and $2197 - 34*64 = 21 $

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Note that you are wrong, as $13^2 \equiv -1 \not \equiv (-1)^2 \pmod {34}$. Note that $$13^{3} \equiv 13^2 \times 13 \equiv 169 \times 13 \equiv (-1) \times 13 \equiv -13 \equiv 21 \pmod {34}$$

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    I have mod 34 not mod 13 (edited) – 2017-02-18
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    @Grisza Stupid typos. I edited. – 2017-02-18
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    yes understand, mind lag stupid retype exponent 2 thx!!! – 2017-02-18
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    Is typing 169 after 13^2 I mean 13^2 * 13 = 169 * 13 is safe way to not to make error? – 2017-02-18
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    @Grisza Typing by hand, generally speaking, is a good way no to make errors. – 2017-02-18