The exponent or "number of times the bases is multiplied by itself" is called the "power".
The vocabulary word you are referring to is "exponentiation." Exponentiation is a mathematical operation that involves raising a base to a certain power or exponent. In exponential notation, the base is multiplied by itself as many times as the exponent indicates. It is often represented as "base^exponent" or "base**exponent." The result of exponentiation is called the "exponential number" or "power" of the base.
