Multiple Choice Power Expressions

Pythagoras theorem is famous in the literature. It works with squares of numbers, i.e., a square of number equals other two numbers with square on each. This paper bring numbers with equality expressions with powers of same order, for example, 7^2:=2^2+3^2+6^2, 6^3:=3^3+4^3+5^3, etc. The work is for the powers from 2 to 6.