To find the numerical equivalent of \( 81 \cdot 83 \), we can use the difference of squares formula, which states:
\[ a^2 - b^2 = (a-b)(a+b) \]
In this case, we can express it as:
\[ 81 \cdot 83 = (82 - 1)(82 + 1) = 82^2 - 1^2 \]
Calculating \( 82^2 \):
\[ 82^2 = 6724 \]
Then calculate \( 1^2 \):
\[ 1^2 = 1 \]
Now subtract these:
\[ 81 \cdot 83 = 82^2 - 1 = 6724 - 1 = 6723 \]
Therefore, the numerical equivalent of \( 81 \cdot 83 \) is \( 6723 \).
Since this isn't included in your options, it seems there was a misunderstanding in interpretation. Therefore, I can clarify that \( 81 \cdot 83 \) equals \( 6723 \) not any of the options you presented.