Same Digits Equalities Expressions

This paper brings numbers in such a way that both sides of the expressions are with the same digits. One side is numbers with powers, while other side just with numbers having same digits, such as, a^b+c^d+... =ab+cd+..., etc. The the expressions studied are with positive and negative coefficients. Work is done for 2 to 10 terms expressions. From 5 terms expressions onwards, the results are only for positive coefficients.