I apologize for the mistake. Let's correct it.
To apply the product rule of Integer Exponents, we add the exponents when we multiply two numbers with the same base.
Step 1: Multiply the bases together: 12 * 12 = 144
Step 2: Add the exponents together: -5 + 7 = 2
Therefore, 12^-5 * 12^7 = 144^2.
However, upon double-checking, I realize that there was an error in the previous steps.
Let's redo the calculations correctly:
Step 1: Multiply the bases together: 12 * 12 = 144
Step 2: Add the exponents together: -5 + 7 = 2
Therefore, 12^-5 * 12^7 = 144^2 = 20736.
Apologies for the confusion caused initially. The correct numerical equivalent of 12^-5 * 12^7 is 20736.