To solve the expression \((3 \cdot 2) \div (7 + 9 - 10)\), we will follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).
-
Evaluate the parentheses:
- Start with the expression \(7 + 9 - 10\).
- First, calculate \(7 + 9 = 16\).
- Then \(16 - 10 = 6\).
Now the expression becomes: \[ (3 \cdot 2) \div 6 \]
-
Evaluate \(3 \cdot 2\): \[ 3 \cdot 2 = 6 \]
Now the expression simplifies to: \[ 6 \div 6 \]
-
Perform the division: \[ 6 \div 6 = 1 \]
Thus, the final answer is: \[ \boxed{1} \]