Question

Select the simplification that accurately explains the following statement. (from clever)

Answer 1

Answer:

OPTION C

Step-by-step explanation:

We know that $(\textbf{x}^{\textbf{a}} )^{\textbf{b}} \hspace{5mm} \textbf{=} \hspace{5mm} \textbf{x}^{\textbf{a . b}}$

Also, $\textbf{x}^{\textbf{a}}. \textbf{x}^{\textbf{a}} \textbf{=} \textbf{x}^{\textbf{a + a}} \textbf{=} \textbf{x}^{\textbf{2a}}$

Using the above two results, we can say that:

$\sqrt{9} = 9^{\frac{1}{2}}$

$\bigg ( 9^{\frac{1}{2}} \bigg )^2 = 9^{\frac{1}{2}}. 9^{\frac{1}{2}}$

$= 9^{\frac{1}{2} + \frac{1}{2}}$            (Using (ii) result)

$= 9^{1} = \textbf{9}$

Hence, OPTION C is the correct answer.