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Setler79 [48]
3 years ago
5

What is the radical form of each of the given expressions?

Mathematics
2 answers:
Lera25 [3.4K]3 years ago
7 0
The main rule to apply here is:

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

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


According to these rules:

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

\displaystyle{ 5^ {\displaystyle{ (\frac{1}{2})} }= \displaystyle{ \sqrt{5^1}=\displaystyle{ \sqrt{5}.

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

\displaystyle{ 3^ {\displaystyle{ (\frac{5}{2})} }= \displaystyle{ \sqrt{3^5}.
Sauron [17]3 years ago
6 0

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

5^{\frac{1}{2}}= \sqrt{5}

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

3^{\frac{5}{2}}= \sqrt{3^5}


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

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

Let us apply same rule in first number

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

5^{\frac{1}{2}}= \sqrt{5}

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

3^{\frac{5}{2}}= \sqrt{3^5}

<h3>Note: When we don't have any number on the top of radical, there 2 is understood.</h3>

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<em>If this was helpful, please mark brainliest. Have a beautiful day.</em>

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