Powers

The idea of multiplication is just to simplify the marking of a sum. For example,     is much easier to read in the form of .  The powers have exactly the same idea:  . Example 1. Let us study the case . We can rewrite the expression in the form of   or in the form   As both are forms of the same original expression, we can say that   Example 2. How about ? . The power in the last term is exactly same as the product of the powers in the original expression. The formulas of powers are expressed as   Based on these formulas, . Example 3.     The same with parameters:                                 Example 4.     Problem 1. Can you explain with words, why ?