Why Expressions with Negative Exponents Equal their Reciprocals
We are familiar with the rule that for a positive exponent ,
In this post, we learn the reason behind the concept of negative exponents and their relationship to the reciprocal of the algebraic expression containing them.
Recall that in dividing an algebraic expression with the same base, we have to subtract their exponents. For example, for
Using this law, it follows that . But
The second equation above is a consequence of this result.
Those are the reasons why expressions with negative exponents equal their reciprocals.