Tetration is an operation in mathematics that is based on iterated, or repeated, exponentiation. It is the fourth in a sequence of basic arithmetic operations, following addition, multiplication, and exponentiation. The exponent "b" in tetration tells you how many times to exponentiate the base. The formal definition of tetration is represented as (^{x}n \equiv n^{n^{n^{.^{.^{.}}}}}), where there are (x) (n)s on the right side of the equation. Tetration is used to represent very large numbers and is denoted by (^ba), where the exponent is to the left of the base. It is important to note that tetration is not commonly used in real-life applications due to the extremely large numbers it produces, which are often impractical to work with.
In summary, tetration is an operation that involves repeated exponentiation and is used to represent very large numbers, but it is not commonly used in practical applications due to the challenges associated with working with extremely large numbers.
