7²⁴-(7³-3) ·(7³+3) ·(7⁶+9) ·(7¹²+81)

To simplify the expression \( 7^{24} - (7^3 - 3)(7^3 + 3)(7^6 + 9)(7^{12} + 81) \), we'll start by recognizing some algebraic identities.

1. Notice that the term \((7^3 - 3)(7^3 + 3)\) can be simplified using the difference of squares: \[ (7^3 - 3)(7^3 + 3) = (7^3)^2 - 3^2 = 7^{6} - 9 \]

2. Now we can rewrite the entire expression: \[ 7^{24} - (7^6 - 9)(7^6 + 9)(7^{12} + 81) \]

3. The term \((7^6 - 9)(7^6 + 9)\) can again be simplified using the difference of squares: \[ (7^6 - 9)(7^6 + 9) = (7^6)^2 - 9^2 = 7^{12} - 81 \]

4. So now our expression is: \[ 7^{24} - (7^{12} - 81)(7^{12} + 81) \]

5. Again, we can apply the difference of squares: \[ (7^{12} - 81)(7^{12} + 81) = (7^{12})^2 - 81^2 = 7^{24} - 6561 \]

6. Now our expression becomes: \[ 7^{24} - (7^{24} - 6561) \]

7. This simplifies to: \[ 7^{24} - 7^{24} + 6561 = 6561 \]

Thus, the final simplified result is: \[ \boxed{6561} \]