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What is [tex]$5^{\frac{2}{3}}$[/tex] in radical form?

A. [tex]\sqrt[3]{25}[/tex]
B. [tex]\sqrt[3]{5}[/tex]
C. [tex]\sqrt{125}[/tex]
D. [tex]\sqrt[3]{125}[/tex]


Sagot :

To find [tex]\( 5^{\frac{2}{3}} \)[/tex] in radical form, follow these steps:

1. Understand the expression [tex]\( 5^{\frac{2}{3}} \)[/tex].
- The exponent [tex]\(\frac{2}{3}\)[/tex] indicates that we are dealing with a power and a root: specifically the cube root (denominator of 3) of [tex]\( 5^2 \)[/tex] (numerator of 2).

2. Rewrite the expression using radical notation:
[tex]\( 5^{\frac{2}{3}} = \sqrt[3]{5^2} \)[/tex].

3. Calculate [tex]\( 5^2 \)[/tex]:
[tex]\( 5^2 = 25 \)[/tex].

4. Substitute [tex]\( 25 \)[/tex] back into the radical form:
[tex]\( 5^{\frac{2}{3}} = \sqrt[3]{25} \)[/tex].

So, [tex]\( 5^{\frac{2}{3}} \)[/tex] in radical form is [tex]\( \sqrt[3]{25} \)[/tex].

Based on the given options:
- [tex]\(\sqrt[3]{25}\)[/tex]
- [tex]\(\sqrt[3]{5}\)[/tex]
- [tex]\(\sqrt{125}\)[/tex]
- [tex]\(\sqrt[3]{125}\)[/tex]

The correct answer is:

[tex]\(\sqrt[3]{25}\)[/tex].