(5xy^7)^3
I'm not sure if I'm doing this write can u tell me if I am?

(5)^3 (x)^3 (y^7)^3
now it gets complicated what do I do after?
do I do this?
125x^37^343
is this correct??

You are half way correct.
When you remove the Whole bracket the powers just gets mutiplied by itself. So its 7*3 = 21.
The Answer is = 125 X^3 Y^21.

got it but y do times 7 x 3=21
y not 7x7x7=343