Answer:
[tex]{3}^{ \frac{3}{2} } = \sqrt[2]{27}[/tex]
Step-by-step explanation:
The given expresion is:
[tex] {3}^{ \frac{3}{2} } [/tex]
Recall the following property:
[tex] {a}^{ \frac{m}{n} } = \sqrt[n]{ {a}^{m} } [/tex]
We compare
[tex] {3}^{ \frac{3}{2} } [/tex]
to
[tex] {a}^{ \frac{m}{n} } [/tex]
We obtain a=3, m=3 and n=2
When we plug these values into the above property, we get:
[tex] {3}^{ \frac{3}{2} } = \sqrt[2]{ {3}^{3} } [/tex]
We simplify this to get:
[tex] {3}^{ \frac{3}{2} } = \sqrt[2]{27} [/tex]
or simply:
[tex]{3}^{ \frac{3}{2} } = \sqrt{27}[/tex]
