What is the answer to this problem {41^{2}+41}{41}=

You need to define what "the answer" would look like.  

It'd be better to ask, "What's the value of this expression?"  

Due to order of operations rules, you MUST evaluate 41^2 first.    1681.

Next, evaluate the addition inside the curly brackets: { 1681 + 41 }.

Result:  1722.  Next, multiply this 1722 by 41 to obtain the final

70602.

Anything inside parentheses has to be done first.  Thus, evaluate 41^2 + 41 first.  Then, mult. your result by 41.