Work out the value of 5^3-5^2:

The first step would be to consider each of the powers individually, work out their value and then proceed with the subtraction to end up with a result. Firstly, as this question is to be done without a calculator, we will remind the principle behind the powers. Say for 5 to the power 3 it is equivalent to writting 5 x 5 x 5. This is also the case for 5 squared i.e. 5 x 5. We would then proceed to work out 5x5 which is 25 and the value for 5 squared and then multiply 25 by 5 once more to obtain 5 cubed which is 125. Now that the hard part is done we simply subtract 25 from 125 (125-25) which gives the final value of 100.