6x3y2

6x3y2 is a string that can have different meanings depending on context. In algebra, it is most commonly interpreted as a compact representation of the monomial formed by multiplying constants and variables, with the variable y raised to the second power.

The standard mathematical interpretation is 6 × x × 3 × y^2, which simplifies to 18xy^2. This term is a monomial with coefficient 18, variables x and y, where x has exponent 1 and y has exponent 2. The total degree of the term is 3 (1 + 2).

As a numerical example, if x = 1 and y = 2, the value is 18 × 1 × 4 = 72. If x = 2 and y = 3, the value is 18 × 2 × 9 = 324. When used on its own, it is a single term in a polynomial and cannot be factored further over the integers.

Ambiguity can arise when the string is taken outside mathematical notation. Without explicit multiplication signs or exponent notation, "6x3y2" could be misread or used as a label or code. In formal mathematics, it is clearer to write 18xy^2 or 18·x·y^2 to avoid confusion. When part of a larger expression, maintaining explicit multiplication and exponent conventions helps ensure correct interpretation.

See also: Monomial, Polynomial, Coefficient, Exponent.