Let's solve the expression step by step:

The expression is:

$6^2 - \frac{20}{2^3 - 3} + 1$

Step 1: Evaluate exponents and parentheses.

• $6^2 = 36$
• $2^3 = 8$

Now the expression becomes:

$36 - \frac{20}{8 - 3} + 1$

Step 2: Simplify inside the fraction.

• $8 - 3 = 5$

So the expression becomes:

$36 - \frac{20}{5} + 1$

Step 3: Divide.

• $\frac{20}{5} = 4$

Now the expression is:

$36 - 4 + 1$

Step 4: Perform addition and subtraction.

• $36 - 4 = 32$
• $32 + 1 = 33$

Final Answer:

$33$

Would you like further details on any of these steps? Here are some related questions to explore:

1. How do you simplify complex fractions?
2. What are the basic rules of order of operations (PEMDAS)?
3. How do exponents affect expressions?
4. How do you work with nested parentheses?
5. What are the common mistakes when solving multi-step problems?

Tip: Always handle exponents and parentheses first when solving expressions using the order of operations (PEMDAS).