Let's simplify the expression step by step:

Given expression:

$(5 + 5^2) \div 5 \cdot 3^2$

Step 1: Simplify the powers

• $5^2 = 25$
• $3^2 = 9$

So the expression becomes:

$(5 + 25) \div 5 \cdot 9$

Step 2: Simplify inside the parentheses

• $5 + 25 = 30$

Now the expression is:

$30 \div 5 \cdot 9$

Step 3: Perform division and multiplication (left to right)

• $30 \div 5 = 6$
• $6 \cdot 9 = 54$

Final Answer:

$54$

Let me know if you'd like more details, or if you have any questions!

Here are 5 related questions you might find interesting:

1. How do we prioritize operations using PEMDAS?
2. What happens if the division and multiplication are reversed in this expression?
3. How would the result change if the exponent was applied after division?
4. Can we use factoring techniques to simplify expressions like this?
5. How does simplifying expressions change in algebraic equations?

Tip: Always simplify powers and parentheses before handling division and multiplication to avoid errors!