A charge of +0.5 C is moved from a position where the electric potential is 10 V to a position where the electric potential is 70 V. What is the the change in potential energy of the charge associated with this change in position?

I am going to scream!

Voltage = change in potential per unit charge.
change in potential energy = q * change in V

so ...

change in PE=.5 times 10v?

sorry my professor didn't cover what C or V equations are

how do you figure out change in V?

is it 10v- 70v? then times it by .5c and get the change in PE??

Yes, 90 volts * .5 coulombs = change in potential energy

45J, correct?

Yes, 60 volts * .5 coulombs = change in potential energy

That is 30 Joules

30J*?

thank you. my professor gave us a change in GPE=mgh and a E=Fe/q equations and was confused

Yes, m g h is joules in gravitational acceleration g

E q = Force (Newtons)
so
E q d = work (Joules) = increase in potential energy
so
E d = increase in potential energy per unit charge which we call V, voltage or electric potential (per Coulomb implied).