Step 1 :\(10^3 \leq 10^6 \Rightarrow \mathrm{com}>\)
Step 2 :\(10^7 > 10000000 \Rightarrow \mathrm{com}>\)
Step 3 :\(10^{-5} \geq 10^{-8} \Rightarrow \mathrm{com}<\)
Step 4 :\(10^{-2} \geq 10^{-9} \Rightarrow \mathrm{com}<\)
Step 5 :x = 2.09 \cdot 10^{10}, y = 5.55 \cdot 10^{12}
Step 6 :x + y = 2.09 \cdot 10^{10} + 5.55 \cdot 10^{12} = 5.550000209 \cdot 10^{12}
Step 7 :x - y = 2.09 \cdot 10^{10} - 5.55 \cdot 10^{12} = -5.54999791 \cdot 10^{12}
Step 8 :x = 8.1 \cdot 10^{23}, y = 4 \cdot 10^{15}
Step 9 :x \cdot y = 8.1 \cdot 10^{23} \cdot 4 \cdot 10^{15} = 32.4 \cdot 10^{38}
Step 10 :x : y = \frac{8.1 \cdot 10^{23}}{4 \cdot 10^{15}} = 2.025 \cdot 10^8
Step 11 :\(\boxed{x+y = 5.550000209 \cdot 10^{12}}\)
Step 12 :\(\boxed{x-y = -5.54999791 \cdot 10^{12}}\)
Step 13 :\(\boxed{x \cdot y = 32.4 \cdot 10^{38}}\)
Step 14 :\(\boxed{x : y = 2.025 \cdot 10^8}\)