Answer :
To express [tex]\(\sqrt[9]{x^7}\)[/tex] in exponential form, we need to understand how to convert a root into an exponent. When you have an expression like [tex]\(\sqrt[n]{x^m}\)[/tex], you can rewrite it as [tex]\(x^{\frac{m}{n}}\)[/tex].
In this problem, we have:
- The expression [tex]\(\sqrt[9]{x^7}\)[/tex].
- The root is 9, and the exponent inside the root is 7.
To convert this into exponential form, we use:
[tex]\[
x^{\frac{m}{n}} = x^{\frac{7}{9}}
\][/tex]
So, [tex]\(\sqrt[9]{x^7}\)[/tex] can be written as [tex]\(x^{\frac{7}{9}}\)[/tex].
Therefore, the correct representation of [tex]\(\sqrt[9]{x^7}\)[/tex] in exponential form is:
[tex]\[ x^{\frac{7}{9}} \][/tex]
Thus, the correct choice is [tex]\(x^{\frac{7}{9}}\)[/tex].
In this problem, we have:
- The expression [tex]\(\sqrt[9]{x^7}\)[/tex].
- The root is 9, and the exponent inside the root is 7.
To convert this into exponential form, we use:
[tex]\[
x^{\frac{m}{n}} = x^{\frac{7}{9}}
\][/tex]
So, [tex]\(\sqrt[9]{x^7}\)[/tex] can be written as [tex]\(x^{\frac{7}{9}}\)[/tex].
Therefore, the correct representation of [tex]\(\sqrt[9]{x^7}\)[/tex] in exponential form is:
[tex]\[ x^{\frac{7}{9}} \][/tex]
Thus, the correct choice is [tex]\(x^{\frac{7}{9}}\)[/tex].
