structural:expansion, structural:scholar_edition, linguistic:voice_change, stylistic:style_transfer
Properties of capital pi notation

By definition,

If all factors are identical, a product of n factors is equivalent to exponentiation:

Associativity and commutativity of multiplication imply

if a is a non-negative integer, or if all x i {\displaystyle x_{i}} are positive real numbers, and

if all a i {\displaystyle a_{i}} are non-negative integers, or if x is a positive real number.