Using an existing pandas df and doing some math on it to create a new pandas df

I have an existing pandas df and I want to create another pandas df by doing some math to the existing pandas df. The existing pandas df is a table usually with ~150 rows, each cell is between 0 and 1 and the sum of each column will add up to somewhere 1.3 to 1.7. I would like to find the exponent to take each cell to so that the column adds up to 1 (or close to it). Then I would like to take each cell to this exponent (the exponent will be unique for each column) and this will give me the new pandas df I am trying to solve for.