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The expression to simplify is:

\[
\frac{3(9 - 3)^4 - 6 \cdot 9 + 7 \cdot 3}{8^3 + 5^2}
\]

### Step-by-Step Simplification

1. **Simplify inside the parentheses:**
   \[
   9 - 3 = 6
   \]
   
2. **Calculate the exponentiation:**
   \[
   (6)^4 = 1296
   \]

   So, the expression becomes:
   \[
   \frac{3 \cdot 1296 - 6 \cdot 9 + 7 \cdot 3}{8^3 + 5^2}
   \]

3. **Compute the multiplication in the numerator:**
   \[
   3 \cdot 1296 = 3888, \quad 6 \cdot 9 = 54, \quad 7 \cdot 3 = 21
   \]
   
   Substitute these values in:
   \[
   \frac{3888 - 54 + 21}{8^3 + 5^2}
   \]

4. **Simplify the numerator:**
   \[
   3888 - 54 = 3834, \quad 3834 + 21 = 3855
   \]

   So, the numerator simplifies to 3855.

5. **Calculate the denominator:**
   \[
   8^3 = 512, \quad 5^2 = 25
   \]
   
   \[
   512 + 25 = 537
   \]

6. **Final expression:**
   \[
   \frac{3855}{537}
   \]

7. **Simplify the fraction:**

   Divide both the numerator and the denominator by their greatest common divisor (GCD), which is 3:
   \[
   \frac{3855 \div 3}{537 \div 3} = \frac{1285}{179}
   \]

### Final Answer

The simplified expression is:

\[
\frac{1285}{179}
\]

Would you like more details on any of the steps, or do you have any questions?

### Additional Related Questions:

1. How do you find the greatest common divisor (GCD) of two numbers?
2. What are the rules for simplifying algebraic expressions with exponents?
3. How can you determine if a fraction can be reduced further?
4. What are some examples of expressions with different bases and exponents?
5. How can you handle expressions that include both multiplication and division?

#### Tip:
When simplifying expressions, always follow the order of operations: parentheses, exponents, multiplication and division (from left to right), addition and subtraction (from left to right).

Simplify the expression 3(9 - 3)^4 - 6 * 9 + 7 * 3 / (8^3 + 5^2)

Learn how to simplify the expression 3(9 - 3)^4 - 6 * 9 + 7 * 3 / (8^3 + 5^2) step-by-step. This problem covers essential arithmetic concepts like exponents, multiplication, and the order of operations. Suitable for students in Grades 8-10.

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