If there were many powers to unite people, then "a power" would be correct.
Being able to unite people is a power. It is only one power. So there is only one power to unite people. It is the power to unite people.
EDIT: @J.R. is correct that there can be many powers to unite people. Let's list some of them:
- Motivational speeches
- Leading by example
- Being a mascot
- Making really cool uniforms
If someone has one of those powers then I can say he has a power to unite people. You could ask which one and I might say he has the power to lead by example.
But there are many ways to lead by example! You could
- Boldly confront bullies
- Be the first person to volunteer
- Show concern for other people
So instead of saying he has the power to lead by example, I could also say he has **a* power to lead by example.
Looking again at uniting people, the fact that someone have a power to unite people also means that the person has the power to unite people. It all depends on how you list the power or powers.