Apply the product rule of integer exponents to find the numerical equivalent of 12^−5⋅12^7

Question

. Show your work and explain how you used the product rule of integer exponents.(2 points) make it super duper super SHORT

Answer 1

To simplify \(12^{-5} \cdot 12^{7}\), we use the product rule of exponents, which states that \(a^m \cdot a^n = a^{m+n}\).

Here, \(m = -5\) and \(n = 7\):

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

Now, calculate \(12^2\):

\[ 12^2 = 144 \]

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