apply the product rule of integer exponents to find the numerical equivalent of 12^-5 x 12^7 show your work and explain how you used the product rule of integer exponents. (2 points)

Answer 1

To apply the product rule of integer exponents to find the numerical equivalent of 12^-5 x 12^7, we can add the exponents when multiplying powers with the same base.

The product rule of integer exponents states that for any non-zero integer a and integers m and n, a^m x a^n = a^(m+n).

In this case, we have 12^-5 x 12^7. Using the product rule, we can add the exponents (m and n) to simplify.

12^-5 x 12^7 = 12^(-5+7)

Since (-5+7) = 2, we have 12^2.

Calculating this numerical value, we have 12 x 12 = 144.

Therefore, 12^-5 x 12^7 is equivalent to 144.