Apply the product rule of integer exponents to find the numerical equivalent equivalent of 12 to the power of -5 times 12 to the power of 7

Answer 1

To find the numerical equivalent of \( 12^{-5} \times 12^{7} \) using the product rule of integer exponents, we apply the rule which states that \( a^m \times a^n = a^{m+n} \).

In this case:

\[ 12^{-5} \times 12^{7} = 12^{-5 + 7} = 12^{2} \]

Now, we calculate \( 12^2 \):

\[ 12^2 = 144 \]

Therefore, the numerical equivalent of \( 12^{-5} \times 12^{7} \) is \( \boxed{144} \).