What is Lifting-the-exponent lemma?

In elementary number theory, the lifting-the-exponent lemma provides several formulas for computing the p-adic valuation ν p {\displaystyle \nu _{p}} of special forms of integers. The lemma is named as such because it describes the steps necessary to "lift" the exponent of p {\displaystyle p} in such expressions. It is related to Hensel's lemma.