Prior to Wallis's formalization of fractional and negative powers, which allowed explicit functions y = x p / q , {\displaystyle y=x^{p/q},} these curves were handled implicitly, via the equations x p = k y q {\displaystyle x^{p}=ky^{q}} and x p y q = k {\displaystyle x^{p}y^{q}=k} (p and q always positive integers) and referred to respectively as higher parabolae and higher hyperbolae (or "higher parabolas" and "higher hyperbolas").