What term describes powers that indicate how many times a number is multiplied by itself?

The term that describes powers indicating how many times a number is multiplied by itself is known as indices. In mathematical contexts, an index (or exponent) refers to the notation used to express repeated multiplication of a number by itself. For example, in the expression (2^3), the base is 2, and the index is 3, which means 2 is multiplied by itself three times (i.e., (2 \times 2 \times 2)).

Indices play a critical role in simplifying expressions and calculating powers, as they provide a clear and concise way to represent multiplication of the same number multiple times. Understanding indices is fundamental in areas such as algebra, calculus, and many applied mathematics disciplines, where powers of numbers frequently appear.

The other terms listed—rational numbers, variables, and integers—do not relate specifically to the concept of powers. Rational numbers refer to fractions or numbers that can be expressed as a ratio of two integers, variables are symbols used to represent numbers in equations, and integers are whole numbers that can be positive, negative, or zero. Hence, the concept of powers is uniquely encapsulated in the term indices.