Respuesta :

The main rule to apply here is:

(i) [tex]\displaystyle{ a^ {\displaystyle{ (\frac{b}{c})} }= \displaystyle{ \sqrt[c]{a^b} [/tex]

(ii)If c=2, then we write the following [tex]\displaystyle{ a^ {\displaystyle{ (\frac{b}{2})} }= \displaystyle{ \sqrt{a^b} [/tex].


According to these rules:

[tex]\displaystyle{ 5^ {\displaystyle{ (\frac{2}{3})} }= \displaystyle{ \sqrt[3]{5^2} [/tex].

[tex]\displaystyle{ 5^ {\displaystyle{ (\frac{1}{2})} }= \displaystyle{ \sqrt{5^1}=\displaystyle{ \sqrt{5}[/tex].

[tex]\displaystyle{ 3^ {\displaystyle{ (\frac{2}{5})} }= \displaystyle{ \sqrt[5]{3^2} [/tex].

[tex]\displaystyle{ 3^ {\displaystyle{ (\frac{5}{2})} }= \displaystyle{ \sqrt{3^5} [/tex].

Answer:[tex]5^{\frac{2}{3}}= \sqrt[3]{5^2}[/tex]

[tex]5^{\frac{1}{2}}= \sqrt{5}[/tex]

[tex]3^{\frac{2}{5}}= \sqrt[5]{3^2}[/tex]

[tex]3^{\frac{5}{2}}= \sqrt{3^5}[/tex]


Step-by-step explanation: According to the rule of exponent of radical form:

[tex]a^{\frac{m}{n} } = \sqrt[n]{a^m}[/tex].

Let us apply same rule in first number

[tex]5^{\frac{2}{3}}= \sqrt[3]{5^2}[/tex]

[tex]5^{\frac{1}{2}}= \sqrt{5}[/tex]

[tex]3^{\frac{2}{5}}= \sqrt[5]{3^2}[/tex]

[tex]3^{\frac{5}{2}}= \sqrt{3^5}[/tex]

Note: When we don't have any number on the top of radical, there 2 is understood.



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