Registering an LPA costs £82. If you're registering 2 LPAs at the same time –  one for financial decisions and one for health and care decisions – then you'd need to pay £82 for each LPA, so £164 in total.
However, if you're on a low annual income (under £12,000), you might be eligible for a 50% discount, and if you're receiving certain income-related benefits you won't have to pay anything at all.