The powerfullest weapon for categoryies are the following:
Dagger: Dragon Dagger (P++)
Longsword: Dragon Longsword
ShortSword: Rune Shortsword
Two-Handed Sword: Saradomin Sword
Godsword: Armadyl Godsword
Battle-Axe: Dragon Battle-Axe
Mace: Dragon Mace
Two-handed Heavy Weapon: Barrelchest Anchior ( Best Value ), Dharoks Greataxe ( Power ).
Scimitar: Dragon Scimitar *Best*
Special Weapon 1: Abyssal Whip *Best*
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The reason there are two bests is because:
Dragon Scimitar can train strength and has a more more useful special attack that blocks prayer for a valuable 5 seconds in combat also value wise.
Abyssal Whip has the same speed as the scimitar, but cost a lot more and can't train strength but however it is the most powerful of the two making it a favourite amongst players with the attack requirements and the money.
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A Weapon
There are Multiple for all basic types of weapons but the grand exchange is the cheapest and has the most variety.
If you have a weapon in your inventory, click on it to wield it. This will un-wield any other weapon you have in your weapon slot.
Any weapon that has a great crush bonus:BattleaxesMacesMaulsWarhammers
I think the most powerful weapon in Skyrim is Daedric Weapon. You can make this by having 90 on skills on smithing and you have to collect a deadric heart and also a couple of leather strips and also a couple of Ebony Ingrots then go to Whiterun and Blacksmith Forge (Located the shop on the right).Hope this helps :)