Question 30

38

To solve the expression 2 x (18 - 14)^2 + 6 using the correct order of operations, we first evaluate the parentheses, followed by the exponent, multiplication, and finally addition. The calculation yields a final result of 38.

A) 22

This option is incorrect because it does not reflect the proper calculations following the order of operations. The value of 22 does not account for the squaring of the result from the parentheses or the multiplication step accurately.

B) 28

Option B is also incorrect. While it may seem plausible, it fails to consider the exponentiation step correctly. The calculation of the expression yields a higher value than 28 due to the squaring of the difference in the parentheses.

C) 38

This is the correct answer. Following the order of operations, we first calculate the expression inside the parentheses as (18 - 14) = 4, then square it to get 16. Multiplying by 2 gives us 32, and adding 6 results in 38.

D) 44

This option is incorrect because it overestimates the result of the expression. It does not accurately follow the order of operations, particularly in the evaluation of the exponent and subsequent addition, leading to an inflated total.

Conclusion

The correct answer is 38, as it correctly follows the order of operations by evaluating the parentheses, then the exponent, followed by multiplication and addition. All other options fail to accurately compute the expression based on these rules, resulting in incorrect values.