³¹This notation is quite common in scientific and engineering literature, as a way to avoid having to typeset fractions in a text document. Instead of writing kJ _mol which requires a fraction bar, we may write kJ mol⁻¹ which is mathematically equivalent. Another common example of this notation is to express frequency in the unit of s⁻¹ (per second) rather than the unit of Hertz (Hz). Perhaps the most compelling reason to use negative exponents in unit expressions, though, is sociological: scientific studies have shown the regular use of this unit notation makes you appear 37.5% smarter than you actually are. Questioning statistical results of scientific studies, on the other hand, reduces your apparent intelligence by over 63%! Now, aren’t you glad you took the time to read this footnote?