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.
To apply the product rule of integer exponents, we need to multiply the bases (12) together and add the exponents (-5 and 7) together.
The product rule states that for any positive integers m and n, and any real number a, a^m * a^n = a^(m+n).
In this case, we have 12^(-5) * 12^7.
Multiplying the bases 12 * 12 gives us 144.
Adding the exponents -5 + 7 gives us 2.
Therefore, 12^(-5) * 12^7 = 144^2.
To find the numerical value of 144^2, we simply square 144.
144^2 = 20,736.
So, the numerical equivalent of 12^-5 * 12^7 is 20,736.