a. If you go one higher with the exponent number (the number that's smaller next to the two), it's basically saying 2 * 2 (if you wanted to do 2^2). If you were to do 2^3, it would be 2*2*2, since exponents means you are multiplying the base number on the exponent number amount of times
b. 2^5 is 2 * 2 * 2 * 2 * 2, which is 4*4*2, making it 32. 2^6 is just 2^5 * 2, so 32 * 2 is 64
c. If you go down from 2^6, you just divide the number by two (or the base number if you were working with some other number)
d. To find 2^0, any number to the power of 0 is always one. If you wanted to find 2^-1, just divide 1 by the base number (which is 2 in this case) and you get 1/2.