Actually it does say it is free on iTunes. Here's MS Word for iOS: https://itunes.apple.com/app/id586447913?mt=8
REQUIREMENTS
iPad Pro: To create or edit documents, you need a qualifying Office 365 subscription* (see http://aka.ms/Office365subscriptions), which also gives you access to the full Office experience.
iPad, iPhone, iPod Touch: To create or edit documents, sign in with a free Microsoft account. To unlock the full Office experience and to access and save documents in OneDrive for Business or on SharePoint, you need a qualifying Office 365 subscription* (see http://aka.ms/Office365subscriptions).
In another similar discussion (that I can't find right now), some users are using it free on their iPad (9.7 screen size). I'm guessing core functionality is free but if you want full functionality, you gotta cough up some $.