To evaluate the expression \( a^4 - b(c) + 2(a) \div 2 \) with the given values \( a = 2 \), \( b = 4 \), and \( c = 3 \), we'll follow the order of operations.
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Substitute the values into the expression: \[ a^4 - b(c) + 2(a) \div 2 = 2^4 - 4(3) + 2(2) \div 2 \]
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Calculate \( 2^4 \): \[ 2^4 = 16 \]
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Calculate \( b(c) = 4(3) \): \[ 4(3) = 12 \]
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Calculate \( 2(a) \div 2 = 2(2) \div 2 \): \[ 2(2) = 4 \quad \text{and} \quad 4 \div 2 = 2 \]
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Now substitute these values back into the expression: \[ 16 - 12 + 2 \]
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Perform the subtraction and addition:
- \( 16 - 12 = 4 \)
- \( 4 + 2 = 6 \)
Thus, the final result is: \[ \boxed{6} \]
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