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.
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.
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