Question

Select the correct answer.

Answer 1

Answer:

OPTION C

Step-by-step explanation:

We have the following rules:

$\sqrt[a]{x} = x^{\frac{1}{a}$    and

$x^a . x^b = x^{a + b}$

OPTION A: $x \sqrt[7]{x}$

= $x . x^{\frac{1}{7}$

= $x^{1 + \frac{1}{7}$

$= x^{\frac{8}{7}$ $\ne x^{\frac{9}{7}$

So, it can be eliminated.

OPTION B: $\bigg ( \frac{1}{\sqrt[7]{x}} \bigg )^9$

= $\bigg ( \frac{1}{x^{\frac{1}{7}}} \bigg )^9$

= $\bigg ( x^ {\frac{-1}{7}} \bigg )^9$

= $x^{\frac{-9}{7}}$

So, this option is also eliminated.

OPTION C: $x . \sqrt[7]{x}$

= $x . x^{\frac{1}{7}}$

= $x^{1 + \frac{1}{7}}$

= $x^{\frac{9}{7}}$

So, OPTION C is the answer.