Question
Apply the product rule of integer exponents to find the numerical equivalent equivalent of 12 to the power of -5 times 12 to the power of 7
Answers
GPT-4o mini
To find the numerical equivalent of \( 12^{-5} \times 12^{7} \) using the product rule of integer exponents, we apply the rule which states that \( a^m \times a^n = a^{m+n} \).
In this case:
\[
12^{-5} \times 12^{7} = 12^{-5 + 7} = 12^{2}
\]
Now, we calculate \( 12^2 \):
\[
12^2 = 144
\]
Therefore, the numerical equivalent of \( 12^{-5} \times 12^{7} \) is \( \boxed{144} \).
In this case:
\[
12^{-5} \times 12^{7} = 12^{-5 + 7} = 12^{2}
\]
Now, we calculate \( 12^2 \):
\[
12^2 = 144
\]
Therefore, the numerical equivalent of \( 12^{-5} \times 12^{7} \) is \( \boxed{144} \).