1) $$100^n = (10^2)^n = 10^{2n}$$
2) $$0,01\cdot 100^{n+3} = 0,01 \cdot (10^2)^{n+3} = 0,01 \cdot 10^{2(n+3)} = 10^{-2} \cdot 10^{2n+6} = 10^{2n+6-2} = 10^{2n+4}$$
3) $$0,01^n : 10^{2-2n} = (10^{-2})^n : 10^{2-2n} = 10^{-2n} : 10^{2-2n} = 10^{-2n - (2-2n)} = 10^{-2n - 2 + 2n} = 10^{-2} $$