To construct an equation that equals 71,647 using numbers up to 23, one approach is to use a combination of multiplication, addition, and subtraction. Here's an equation that satisfies these conditions:

$23^4 + 23^3 + 23 \times 20 + 23 \times 18 - 23 = 71,647$

Let's break it down:

1. $23^4 = 279,841$
2. $23^3 = 12,167$
3. $23 \times 20 = 460$
4. $23 \times 18 = 414$
5. Subtract $23$ from the total sum to get the final value.

Adding these terms and subtracting $23$ gives:

$279,841 + 12,167 + 460 + 414 - 23 = 71,647$

Would you like a detailed breakdown of how this equation was constructed, or do you have any other questions?

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Relative Questions:

1. How can different exponents be used to generate larger numbers?
2. What are some other ways to reach a specific number using limited operations?
3. How does the choice of the base number influence the result in exponentiation?
4. What are some practical applications of forming specific numbers through equations?
5. Can you explain how combining basic operations can yield a target number?

Tip: Experimenting with exponentiation can quickly generate large numbers, making it useful for constructing equations to match specific targets.