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].
