Ok so when working with powers we basically times the number by itself. So since it's 0.5 to the third power, we'd multiply 0.5 by itself 3 times.
So 0.5 x 0.5 x 0.5 is equal to 0.125
And for the second problem, what helps me is to turn the fraction into a decimal. To do that you divide the numerator by the denominator
1 divided by 8 is 0.125
So keep in mind 1/8 is the same as 0.125.
So 0.125 multiplied by 0.125 is 0.015625
But if you want to keep it as a fraction
1/8 multiplied by 1/8 is 1/64.
I hope this helps :)