Alright, let's work through the expression step-by-step.
We need to evaluate the expression [tex]\(\left(7^{1/2}\right)^2\)[/tex].
First, recognize that [tex]\(7^{1/2}\)[/tex] represents the square root of 7, which we can denote as [tex]\(\sqrt{7}\)[/tex]. So the expression [tex]\(\left(7^{1/2}\right)^2\)[/tex] can be rewritten as:
[tex]\[
\left(\sqrt{7}\right)^2
\][/tex]
Square roots and squares are inverse operations, meaning that taking the square of the square root of a number will give you the original number back. Hence:
[tex]\[
\left(\sqrt{7}\right)^2 = 7
\][/tex]
Thus, the value of the expression [tex]\(\left(7^{1 / 2}\right)^2\)[/tex] is 7.
So, the correct answer is:
B. 7
