Definition:Power (Algebra)/Rational Number/Historical Note

Historical Note on Rational Power

The definition:

$x^r = x^{p/q} = \left({\sqrt [q] x}\right)^p = \sqrt [q] {\left({x^p}\right)}$

is due to Nicole Oresme circa $1360$.

The concept of a fractional exponent was reintroduced by John Wallis in the $17$th century.

Sources

• 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {B}.12$: Wallis's Product: Footnote $1$
• 1997: Donald E. Knuth: The Art of Computer Programming: Volume 1: Fundamental Algorithms (3rd ed.) ... (previous) ... (next): $\S 1.2.2$: Numbers, Powers, and Logarithms