Question

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.
Do it in the least amount of sentences as possible.

Answer 1

Do it in a sentence.

Answer 2

To find the numerical equivalent of \( 12^{-5} \cdot 12^{7} \), we apply the product rule of integer exponents, which states that \( a^m \cdot a^n = a^{m+n} \). Here, \( a = 12 \), \( m = -5 \), and \( n = 7 \).

Thus, we have:

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

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

\[
12^{2} = 144
\]

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

Answer 3

Using the product rule of integer exponents, \( 12^{-5} \cdot 12^{7} = 12^{(-5 + 7)} = 12^{2} = 144 \).