Apply the product rule of integer exponents to find the numerical equivalent of 12^−5⋅12^7. Show your work and explain how you used the product rule of integer exponents.

Question

make it 3-5 senteces and to sound like a 7th grader

Answer 1

To solve \( 12^{-5} \cdot 12^7 \), we can use the product rule of integer exponents. The product rule says that when we multiply two powers with the same base, we add their exponents. So, we add \(-5\) and \(7\):

\[ -5 + 7 = 2. \]

Now, we rewrite it as \( 12^2 \). To find the numerical equivalent, we calculate \( 12^2 \), which is \( 12 \times 12 = 144 \). So, \( 12^{-5} \cdot 12^7 = 144 \).