IPA: /ɪnˈdɒmɪtəblnəs/
KK: /ɪnˈdɑːmɪtəblnəs/
The quality of being impossible to defeat or overcome; showing great determination and resilience.
Her indomitableness in the face of adversity inspired everyone around her.
Indomitableness is formed from "in-" (meaning not), "domitare" (from Latin, meaning to tame), and "-ness" (meaning the state of being). The word describes the state of being not able to be tamed or subdued.
Think of 'not' ('in-') being able to 'tame' ('domitare') something, which helps you remember that indomitableness means the state of being untamable.