Some of the sentences in this activity should be completed with the verbs conjugated in the "subjunctive" form. The subjunctive form is used in Spanish whenever the sentence expresses a wish, hope, or some sort of doubt. Basically in Spanish when you talk about something that is not certain to happen, this form of the verb is used to express that uncertainty. Each of these is conjugated in the present form of the subjunctive form.
1. nosotros podamos
4. (ellos) vivan
6. (ello; Because el mundo is singular) tenga
The verbs in sentences 2, 3, and 5 can remain in the infinitive because of the sentence construction.
2. El sueño de mi vida es vivir en un mundo sin guerras.
Here, since the verb ser is already conjugated to es we can keep vivir in the infinitive.
3. Tengo la esperanza de ser la primera presidenta de Estados Unidos.
5. Quiero ser hombre de negocios. Una de mis grandes ambiciones es construirfábricas que no contaminen el aire.