To determine which expression is equal to [tex]\(3^{\frac{3}{2}}\)[/tex], let’s evaluate [tex]\(3^{\frac{3}{2}}\)[/tex] step by step.
First, recognize that [tex]\(3^{\frac{3}{2}}\)[/tex] can be interpreted as the square root of [tex]\(3^3\)[/tex]:
[tex]\[
3^{\frac{3}{2}} = \left(3^3\right)^{\frac{1}{2}}
\][/tex]
Calculate [tex]\(3^3\)[/tex]:
[tex]\[
3^3 = 27
\][/tex]
Now take the square root of 27:
[tex]\[
\left(3^3\right)^{\frac{1}{2}} = \sqrt{27}
\][/tex]
Therefore, [tex]\(3^{\frac{3}{2}} = \sqrt{27}\)[/tex].
The correct answer is:
[tex]\(\sqrt[2]{27}\)[/tex]
