I tried multiplying 11 times seven times with itself (same as the exponent)
First, I do it three times
$11*11*11=1331$
then I exceed 697.
Each time when exceeding 697, I divided by 697
$\frac{1331}{697}=1,$ remainder 634
noted the remainder and kept repeating the same procedure, until I reached the final result of 445.
Reason for this: One avoids to have too big numbers this way.
This way is somehow simple, but still tedious. Are you aware about any tricks that could help solve such modular arithmetic problems generally (that can also be applied in time-constrained situations)?
