Solve 18-((560÷(70/3)-14)-9): Order of Operations Challenge

To solve this problem, we'll follow these steps:

• Step 1: Calculate the division inside the innermost parentheses: $560 : \frac{70}{3}$.
• Step 2: Use the reciprocal to perform division: Rewrite as $560 \times \frac{3}{70}$.
• Step 3: Continue simplifying the expression from inside to outside.

Now, let's work through each step:
Step 1: Evaluate $560 : \frac{70}{3}$. This is equivalent to $560 \times \frac{3}{70}$.
Step 2: Perform the multiplication: $(560 \times 3) / 70 = 1680 / 70 = 24$.
Step 3: Simplify $24 - 14$. This results in $10$.
Step 4: Calculate $10 - 9$. This equals $1$.
Step 5: Subtract this from 18: $18 - 1 = 17$.

Therefore, the answer to the problem is $17$.