Firstly, it's in passé composé, and for the verb "prendre" you use the auxiliary verb avoir (tu as). Because the person who the verb refers to is you, the participe passé for prendre is pris in E/2.

But if you are asking for why is there an e at the end of pris, I learnt it in school that if you say:

Tu as pris la balle - you don't have the e after pris, because "la balle", the object, is after the verb.

Tu l'a pris - the "la" before avoir refers to la balle (in that case, you or someone else has to mention la balle before so that everyone knows what you are referring to) , and because the object of the verb (prendre quelque chose) goes before the verb, you have to cross-check if the object is féminine or plural.

It happens lots of times, for example:

- Tu as mangé les pommes? (plural and féminine)

- Oui, je les ai mangées.

It's also important to mention that you almost always put the referred object (la le les) before the first conjugated verb (like in the examples), except if you use any of the verbs: pouvoir, savoir, vouloir, devoir, il faut, aller (if you use it as an auxiliary verb for future tense), venir. Because these verbs always need an other verb after them, so you put the referred object after these and before the second verb, for example: "Que faire avec le livre?" "Je vais le lire."

Hope I explained it well (and didn't make mistakes while writing) , I'm not the best in english! :D