Apply the product rule of integer exponents to find the numerical equivalent of 12−5⋅127

Question

12
−
5
⋅
12
7
. Show your work and explain how you used the product rule of integer exponents.(2 points) simplify it 3 sentences

Answer 1

To simplify \( 12^{-5} \cdot 12^7 \), we can apply the product rule of integer exponents, which states that when multiplying like bases, we add their exponents. Here, we have:

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

Now, calculating \( 12^2 \) gives us \( 144 \). Thus, the numerical equivalent of \( 12^{-5} \cdot 12^7 \) is \( 144 \).