To evaluate the expression \( 4 \div 2 - 4^2 \), we need to 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)).
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Exponents: Calculate \( 4^2 \). \[ 4^2 = 16 \]
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Division: Next, perform the division \( 4 \div 2 \). \[ 4 \div 2 = 2 \]
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Subtraction: Now subtract \( 16 \) from \( 2 \). \[ 2 - 16 = -14 \]
So, the value of the expression \( 4 \div 2 - 4^2 \) is \(\boxed{-14}\).