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

Question

. Show your work and explain how you used the product rule of integer exponents. short it and 8th grader sentences

Answer 1

To find the numerical equivalent of \( 12^{-5} \cdot 12^7 \), we can use the product rule of integer exponents. The product rule says that when you multiply two numbers with the same base, you can add their exponents.

Here's how we do it step by step:

1. Identify the base: Here, the base is \( 12 \).
2. Write the exponents: We have \( -5 \) and \( 7 \).
3. Apply the product rule: \[ 12^{-5} \cdot 12^7 = 12^{-5 + 7} = 12^{2} \]

Now, we just need to calculate \( 12^2 \): \[ 12^2 = 12 \cdot 12 = 144 \]

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

In summary, we used the product rule to combine the exponents and found that \( 12^{-5} \cdot 12^7 = 12^2 = 144 \).