>!With your fortify alchemy enchanted gear equipped, activate the alchemy table. Your Alchemy skill of 50s is fine, but 100 will be max strength, but you could always add a loop for more powerful potions. You will also need Alchemy perks applied in Alchemist (at least 2/5) and Benefactor is a must. Less enchants at lower numbers works as well) (the standard Enchanting 100 cap is helm, arms, ring, necklace for 25% Fortify Alchemy each, totaling 100%.
What you will need, is equipment with alchemy enchants. (vanilla Skyrim only, this will not work with unofficial patches applied) Lots of good info in the posts here, but no one has actually mentioned restoration looping, which would be those 'extremely powerful' potions.
Poke an enemy with a dagger and watch them instantly collapse as their health bar leaks to zero. At alchemy 100 with enchanted garments, you'll have a potion pushing 30 seconds of paralysis and insane damage. All of those can be grown at home and it provides lingering damage and paralysis. Once you get strong enough, I strongly recommend Imp Stool, Mora Tapinella, and Canis Root. Buy apothecaries out of their stock and sell however much you can. The good thing about alchemy is that buying ingredients turns a profit very quickly. Hit up the clothing shop (radiant raiment?) In Solitude for alchemy boosting gear and a fantastic apothecary right across the street. Will barely give you any XP relative to a crappy fortify health. An incredibly potent poison, while extremely useful. The most important thing to keep in mind is that leveling is based only on the gold value of the potion. My advice is to make every potion with every ingredient to the best of your ability so you have the whole cookbook in your menus. There are several websites and apps you can look up to find values and recipes. Hearthfire is extremely helpful because you can griw your own ingredients. Combine it with any other skill and that skill becomes god-tier without any exploits.
Imo, alchemy is the single best skill in the game.