Question

even if it takes 10 years, i will learn to play the piano. gerund infinitive participle

Explanation:

In the sentence "Even if it takes 10 years, I will learn to play the piano", the phrase "to play" is an infinitive. An infinitive is formed by "to" + the base form of a verb. A gerund is a verb - ing form used as a noun, and a participle is a verb - ing or verb - ed form used as an adjective or in verb tenses (like present participle in continuous tenses or past participle in perfect tenses). Here, "to play" follows the structure of an infinitive.

Answer:

infinitive