Solve: (3²+2²)² ÷ (√256-√9) - √9·√9 | Complex Expression Challenge

The given expression is: $(3^2+2^2)^2:(\sqrt{256}-\sqrt{9})-\sqrt{9}\cdot\sqrt{9}$

Let's solve it step by step:

Step 1: Solve inside the parentheses

Calculate $3^2$ and $2^2$:

• $3^2 = 9$
• $2^2 = 4$

Add the results: $9 + 4 = 13$

Now, the expression becomes $(13)^2 : (\sqrt{256} - \sqrt{9}) - \sqrt{9}\cdot\sqrt{9}$

Step 2: Calculate the powers and roots

• $(13)^2 = 169$
• $\sqrt{256} = 16$
• $\sqrt{9} = 3$

Substitute these back into the expression: $169 : (16 - 3) - 3\cdot3$

Step 3: Simplify the expression

• The expression in the parentheses: $16 - 3 = 13$

Now the expression is: $169 : 13 - 9$

Step 4: Perform division

Divide $169$ by $13$:

• $169 : 13 = 13$

Now the expression is: $13 - 9$

Step 5: Perform subtraction

Subtract $9$ from $13$:

• $13 - 9 = 4$

The final answer is $4$.