Which expression is undefined over the real numbers?

Rationale

(-7)^(1/2)

Taking the square root of a negative number results in an undefined expression over the real numbers, as real numbers do not accommodate square roots of negatives. Therefore, (-7)^(1/2) is not defined in the real number system.

A ((-3)^0) YOUR ANSWER

Any non-zero number raised to the power of zero equals one. Thus, (-3)^0 is equal to 1, which is well-defined over the real numbers.

B (0/4) YOUR ANSWER

Dividing zero by any non-zero number yields zero. Therefore, 0/4 is equal to 0, a defined value in the real number system.

C (|-2|) YOUR ANSWER

The absolute value of a number is always defined, as it represents the non-negative distance of that number from zero. Thus, |-2| equals 2, which is a defined expression.

D ((-7)^(1/2)) CORRECT

Taking the square root of a negative number like -7 is not defined within the real numbers, as it would require the use of imaginary numbers. Consequently, this expression is undefined.

Conclusion

Among the given choices, (-7)^(1/2) stands out as the only expression that is undefined over the real numbers due to the square root of a negative number. In contrast, the other choices are well-defined and yield valid real number results. Understanding these distinctions is crucial for navigating expressions in algebra and calculus.

Which expression is undefined over the real numbers?

(-7)^(1/2)

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