Arrange Mathematical Operation Using 0-9 to Match the Post Number

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Participants are tasked with arranging the digits 0-9 to create mathematical expressions that equal the post number, adhering to three specific rules: no double posting, no approximations, and no invented variables. The thread begins with an example that successfully results in the number 1 using the expression "94875326 x 0 + 1." Subsequent posts follow suit, showcasing various calculations that yield the corresponding post numbers, such as "34,567,892^0 + 1 = 2" and "0·1 + (3 - 2) + (5-4) + (7-6) + (9-8) = 4." The challenge encourages creativity and mathematical thinking while fostering engagement among participants. Overall, the thread promotes a fun and interactive way to explore mathematical operations.
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In this puzzle, you use all integers from 0 to 9 to arrange a mathematical calculation whose result is the post number. There are only three rules:
1. No double posting
2. No approximation
3. No made-up variables
Now since it is the first post here, let me do it first which results in 1:
94875326 x 0 + 1= 1
Let's the fun begin! *say it in Sakaki Yuya's style*
 
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$34,567,892^0 + 1 = 2$
 
$34,567,891^0 + 2 = 3$
 
$0\cdot 1 + (3 - 2) + (5-4) + (7-6) + (9-8) = 4$
 
$34,267,891^0 + 5 = 5$
 
Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?

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