Ἐξομολογοῦμαί [2 verses](1st sg pres ind mp ) "I thank " is from exomologeo, which means "to confess," "to admit," and "to acknowledge." Christ is not thanking God here but admitting a truth.  - The Greek word translated as "thank" really means "to confess," "to admit," and "to acknowledge." It is in the form where the subject is either being acted upon or acts on himself. Christ is confessing himself to God here, acknowledging something about himself.

ἐξώτερον: [3 verses](adj sg neut acc) "Outer" is exoteros, which means "outer" and "utter," and literally means "more outside."  - - The word translated as "outer" is the adjective that means "more outside," but it is preceded by an article, so it acts as a noun, "the outside."

ἔξωθεν [8 verses](adv) "Outwardly"is exothen, which "from without" and "outward." -- The word used for "outwardly" is the adverb meaning "outwardly" and "from without."

ἐξουδενηθῇ; [1 verse] ( verb 3rd sg aor subj pass ) "Set to naught" is exoudeneo, which is a word only used in the Gospels, but it is a verb from from group of related words (exoudenôma, exoudenôsis, exouthenêma, exoudenismos), which mean "contempt" and an "object of contempt".  - -- "Set to naught" is  a verb Jesus only uses here in the Gospels. It is a verb from of words that mean "contempt" and an "object of contempt." These sense in English is "despise." In the Septuagint, this verb is used to translate the Hebrew bawsaw (בָּזָה), which is usually translated as "despised."

ἐξουσίαν [23 verses](noun sg fem acc) "Power" is exousia which means "control," "the power of choice," "permission," "the power of authority," "the right of privilege," "abundance of means," and "abuse of power." -- (WW) The term translated as "power" means "authority," "control," and "the ability to choose." To avoid confusing it with the other Greek word for energy "power" from which we get "dynamic," this word is best translated as "authority" or "control." See this article on power and authority. WW --Wrong Word -- The word translated as "power" should be something more like "authorities."