Answer:
[tex]5^{\frac{1}{2} } =\sqrt{5}[/tex]
Step-by-step explanation:
Here we need to use the following property
[tex]x^{\frac{a}{b} }=\sqrt[b]{x^{a} }[/tex]
So, we use this property to rewrite the given expression
[tex](5^{\frac{3}{4} } )^{\frac{2}{3} }[/tex]
First, we multiply exponents to have only one
[tex](5^{\frac{3}{4} } )^{\frac{2}{3} }=(5)^{\frac{3 \times 2}{4 \times 3} }=(5)^{\frac{6}{12} }=5^{\frac{1}{2} }[/tex]
Then, we apply the property to rewrite the expression
[tex]5^{\frac{1}{2} } =\sqrt{5}[/tex]
Therefore, the right answer is the third choice.
