Why do you subtract exponents when dividing powers with the same base

Remember, exponents are related to multiplication not addition. The base is the number you are multiplying however many times the exponent tells you to. When you are dividing, you are taking away the amount of times being multiplied. This decreases the exponent value.
For example:

3³/3² 

3 · 3 · 3
3 · 3

= 3

3 cubed 

When you divide 3³ by 3², you are taking two of the 3's out of 3 · 3 · 3 which results in just one 3.

(1/x + 1)^2 + 6 (1/x + 1) +5