Answer:
OPTION C
Step-by-step explanation:
We have the following rules:
[tex]$ \sqrt[a]{x} = x^{\frac{1}{a} $[/tex] and
[tex]$ x^a . x^b = x^{a + b} $[/tex]
OPTION A: [tex]$ x \sqrt[7]{x} $[/tex]
= [tex]$x . x^{\frac{1}{7} $[/tex]
= [tex]$ x^{1 + \frac{1}{7} $[/tex]
[tex]$ = x^{\frac{8}{7} $[/tex] [tex]$ \ne x^{\frac{9}{7} $[/tex]
So, it can be eliminated.
OPTION B: [tex]$ \bigg ( \frac{1}{\sqrt[7]{x}} \bigg )^9 $[/tex]
= [tex]$ \bigg ( \frac{1}{x^{\frac{1}{7}}} \bigg )^9 $[/tex]
= [tex]$ \bigg ( x^ {\frac{-1}{7}} \bigg )^9 $[/tex]
= [tex]$ x^{\frac{-9}{7}} $[/tex]
So, this option is also eliminated.
OPTION C: [tex]$ x . \sqrt[7]{x} $[/tex]
= [tex]$ x . x^{\frac{1}{7}} $[/tex]
= [tex]$ x^{1 + \frac{1}{7}} $[/tex]
= [tex]$ x^{\frac{9}{7}} $[/tex]
So, OPTION C is the answer.
