Question 24

(-7)^(1/2) is undefined over the real numbers.

The expression (-7)^(1/2) represents the square root of -7, which cannot be calculated within the set of real numbers as square roots of negative numbers are not defined in this system.

A) (-3)^0

The expression (-3)^0 equals 1, as any non-zero number raised to the power of zero is defined to be 1. Therefore, this option is defined over the real numbers.

B) 0/4

The expression 0/4 equals 0, as dividing zero by any non-zero number is defined and results in zero. Thus, this option is also defined over the real numbers.

C) |-2|

The expression |-2| represents the absolute value of -2, which is equal to 2. Absolute values are always defined for real numbers, making this option valid.

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

This expression is undefined because it involves taking the square root of a negative number. In the real number system, there are no real solutions to this expression, rendering it undefined.

Conclusion

The expression (-7)^(1/2) is the only option that is undefined over the real numbers, as it attempts to calculate the square root of a negative value. All other options are valid expressions that yield defined results within the real number system.