Answer:
Given an algebraic expression involving exponents
so, we can write it in radical form based on the fact that is [tex]x^{\frac{a}{n}}[/tex] equivalent to the nth root of [tex]x^a[/tex]
i.e, [tex]x^{\frac{a}{n}} =\sqrt[n]{x^a}[/tex]
Also, Use the following rule of exponents : [tex](x^a)^b = x^{ab}[/tex]
then:
1. [tex]5^{\frac{2}{3}}[/tex] =[tex](5^2)^{\frac{1}{3} }[/tex]= [tex]\sqrt[3]{5^2}[/tex]
2. [tex]5^{\frac{1}{2} }[/tex] = [tex]\sqrt{5}[/tex]
3. [tex]3^{\frac{2}{5}} = (3^2)^{\frac{1}{5} } = \sqrt[5]{3^2}[/tex]
4. [tex]3^{\frac{5}{2}} = (3^5)^{\frac{1}{2}} =\sqrt{3^5}[/tex]
