Question

Find the numerical equivalent of 81⋅83
.(1 point)
Responses

84
8 superscript 4 baseline

4,096
4,096

520
520

512

Answer 1

To find the numerical equivalent of \( 81 \cdot 83 \), we can use the identity for the product of two numbers that are equidistant from a midpoint:

\[
a^2 - b^2 = (a - b)(a + b)
\]

In this case, we can express it around the average of the two numbers:

Let \( a = 82 \) (the midpoint) and express the two numbers as:

\[
81 = 82 - 1 \quad \text{and} \quad 83 = 82 + 1
\]

Using the identity:

\[
81 \cdot 83 = (82-1)(82+1) = 82^2 - 1^2
\]

Calculating \( 82^2 \):

\[
82^2 = 6724
\]

Now substituting back into the equation:

\[
81 \cdot 83 = 6724 - 1 = 6723
\]

The value \( 6723 \) doesn't seem to be among the provided options, suggesting a different approach or identifying potential typographical errors.

However, looking through these responses doesn't yield a reconciliation with any logical transformations or breakdowns into factors that lead us to interpret them numerically to equal 81 * 83. Thus I would suggest recalculation in instances or a review for miscalculations throughout for further arrangements.

Final calculation:

\[
81 \cdot 83 = 6723
\]

None of the options provided aligns with the calculated value from direct multiplication. Please check the values or representational formats for potential decimal shifts.