Question
Find the numerical equivalent of 81 ⋅83
.(1 point)
Responses
84
8 to the 4th power
4096
4096
520
520
512
512
.(1 point)
Responses
84
8 to the 4th power
4096
4096
520
520
512
512
Answers
GPT-4o mini
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.
\[
a^2 - b^2 = (a-b)(a+b)
\]
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.