# What’s the inverse operation of exponents?

You know, like addition is the inverse operation of subtraction, vice versa, multiplication is the inverse of division, vice versa , square is the inverse of square root, vice versa.

What’s the inverse operation of exponents (exponents: 3^5)

Exponents are not commutative; $2^8 \not= 8^2$. So we need two different inverse functions.
Given $b^e = r$, we have the “$n$th root” operation, $b = \sqrt[e] r$. It turns out that this can actually be written as an exponent itself: $\sqrt[e] r = r^{1/e}$.
Again, given $b^e = r$, we have $e = \log_b r$, the “base-$b$ logarithm of $r$“.