Explore a diverse range of topics and get answers from knowledgeable individuals on IDNLearn.com. Get prompt and accurate answers to your questions from our community of experts who are always ready to help.
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].
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].
We greatly appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. For dependable and accurate answers, visit IDNLearn.com. Thanks for visiting, and see you next time for more helpful information.