Answer :
To convert the given expression [tex]\(\sqrt[9]{x^7}\)[/tex] into exponential form, we follow these steps:
1. Understand the radical notation: [tex]\(\sqrt[9]{x^7}\)[/tex] means "the 9th root of [tex]\(x^7\)[/tex]."
2. In exponential form, a radical of the form [tex]\(\sqrt[n]{x^m}\)[/tex] can be expressed as [tex]\(x^{\frac{m}{n}}\)[/tex].
3. Apply this to the given expression:
- Here, [tex]\(m = 7\)[/tex] and [tex]\(n = 9\)[/tex].
4. Substitute these values into the formula: [tex]\(x^{\frac{m}{n}} = x^{\frac{7}{9}}\)[/tex].
Therefore, [tex]\(\sqrt[9]{x^7}\)[/tex] in exponential form is [tex]\(x^{\frac{7}{9}}\)[/tex].
The correct answer from the options provided is:
- [tex]\(x^{\frac{7}{9}}\)[/tex]
1. Understand the radical notation: [tex]\(\sqrt[9]{x^7}\)[/tex] means "the 9th root of [tex]\(x^7\)[/tex]."
2. In exponential form, a radical of the form [tex]\(\sqrt[n]{x^m}\)[/tex] can be expressed as [tex]\(x^{\frac{m}{n}}\)[/tex].
3. Apply this to the given expression:
- Here, [tex]\(m = 7\)[/tex] and [tex]\(n = 9\)[/tex].
4. Substitute these values into the formula: [tex]\(x^{\frac{m}{n}} = x^{\frac{7}{9}}\)[/tex].
Therefore, [tex]\(\sqrt[9]{x^7}\)[/tex] in exponential form is [tex]\(x^{\frac{7}{9}}\)[/tex].
The correct answer from the options provided is:
- [tex]\(x^{\frac{7}{9}}\)[/tex]
