Apply the product rule of integer exponents to find the numerical equivalent of 12-^5 • 12^7 .

1 answer

To find the numerical equivalent of \( 12^{-5} \cdot 12^{7} \), we can use the product rule of exponents, which states that when multiplying two powers with the same base, you add the exponents:

\[ a^m \cdot a^n = a^{m+n} \]

In this case, the base \( a \) is 12, \( m = -5 \), and \( n = 7 \). Applying the product rule:

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

Now, we can calculate \( 12^{2} \):

\[ 12^{2} = 144 \]

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