RSA encryption question

Jan 2016
the RSA public key is 2183,895, i have found my decoding key to be D=7, now I am given that the resulting cyphertext is y=821, i have to find the encrypted number 7 using this.

First of all is my decoding key d=7 correct?

Using this I have the equation x is congruent to 821^(7)mod2183.

my question is how am i supposed to find x for such a large number in the remainder??

I was thinking that y=y*y^(2)*y^(4) and maybe we could use this property as a shortcut ??