Apply the product rule of integer exponents to find the numerical equivalent of 12^-5 * 12^7 show your work and explain how you used the product of integer exponents.

Answer 1

The product rule of integer exponents states that when you multiply two terms with the same base, you add their exponents. In this case, we have 12^-5 * 12^7.

To apply the product rule, we add the exponents together: -5 + 7 = 2.

So, 12^-5 * 12^7 is equivalent to 12^2.

Now let's find the numerical value of 12^2. 12^2 means we multiply 12 by itself, twice:

12^2 = 12 * 12 = 144.

Therefore, the numerical equivalent of 12^-5 * 12^7 is 144.