Exponentiation vs. Tetration — What's the Difference?

Exponentiation is a mathematical operation, written as bn, involving two numbers, the base b and the exponent or power n, and pronounced as "b (raised) to the (power of) n". When n is a positive integer, exponentiation corresponds to repeated multiplication of the base: that is, bn is the product of multiplying n bases: The exponent is usually shown as a superscript to the right of the base.

In mathematics, tetration (or hyper-4) is an operation based on iterated, or repeated, exponentiation. There is no standard notation for tetration, though ↑↑ {\displaystyle \uparrow \uparrow } and the left-exponent xb are common.

The act of raising a quantity to a power.

(arithmetic) The arithmetic operator consisting of repeated exponentiation, by analogy with exponentiation being repeated multiplication and multiplication being repeated addition, ^ba denoting a to the power of a to the power of ... to the power of a, in which a appears b times. Notation: ^ba, a↑↑b or a→b→2

The process of calculating a power by multiplying together a number of equal factors, where the exponent specifies the number of factors to multiply.

A mathematical problem involving exponentiation.

The process of raising a quantity to some assigned power.

The process of raising a quantity to some assigned power