10n

10n denotes the product of the scalar 10 and a variable n. In mathematics, it is read as “ten n” or “ten times n” and represents a linear expression in n. If n is an integer, 10n is a multiple of 10. If n is a real number, 10n is simply a real number scaled by 10. The function f(n) = 10n is a linear function with slope 10 and intercept 0.

Algebraic properties of 10n follow standard rules of multiplication. For any numbers n and m, 10(n + m) = 10n + 10m, and (10n)m = 10(nm). The expression can be used to combine like terms: for example, 10n + 5n = 15n. When n is a natural number, 10n is a positive multiple of 10.

Examples illustrate the concept: if n = 3, then 10n = 30; if n = -4, then 10n = -40. In computer science and complexity analysis, a term like 10n is often treated as having the same growth rate as n, since constant factors are typically ignored, so 10n is O(n).

In summary, 10n is a simple linear expression representing ten times a variable, with straightforward arithmetic and algebraic properties that apply across integers and real numbers. It is widely used to express scaled quantities, multiples of ten, and linear relationships.