Question

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

4,096
4,096 - no response given

84
8 to the 4th power - incorrect

520
520 - no response given

512

Answer 1

To find the numerical equivalent of \( 81 \cdot 83 \), we can use the difference of squares formula, which states that:

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

Here, let's note that \( 81 \) and \( 83 \) can be expressed using numbers around \( 82 \):

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

Now, we can rewrite the product:

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

This follows the difference of squares:

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

Calculating \( 82^2 \):

\[
82^2 = 6724
\]

Now, subtract \( 1 \):

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

However, since none of the provided answers match direct arithmetic calculations, we will recognize the actual product \( 81 \cdot 83 \) as \( 81 \cdot 83 \) giving \( 6723 \), which indicates no provided answers fit.

Looking at provided choices, they seem to shift focus onto values or powers that do not concern \( 81 \cdot 83 \) itself. Therefore, without a clear match, we can conclude:

**None of the provided responses (4,096; 84; 520; 512) is the numerical equivalent of \( 81 \cdot 83 \).**