Notation
In expressions such as, the notation for exponentiation is usually to write the exponent as a superscript to the base number . But many environments — such as programming languages and plain-text e-mail — do not support such two-dimensional layout. People have adopted the linear notation for such environments; the up-arrow suggests 'raising to the power of'. If the character set doesn't contain an up arrow, the caret ^ is used instead.
The superscript notation doesn't lend itself well to generalization, which explains why Knuth chose to work from the inline notation instead.
Read more about this topic: Knuth's Up-arrow Notation