To find the expression that is equivalent to [tex]\(\sqrt{\sqrt{\sqrt{x^{48}}}}\)[/tex], we need to simplify the given expression step by step. Let's break it down:
1. Start with the innermost radical:
[tex]\[
\sqrt{x^{48}}
\][/tex]
Rewriting the square root as an exponent, we have:
[tex]\[
(x^{48})^{1/2}
\][/tex]
This simplifies to:
[tex]\[
x^{48 \cdot \frac{1}{2}} = x^{24}
\][/tex]
2. Next, we take the square root of [tex]\(x^{24}\)[/tex]:
[tex]\[
\sqrt{x^{24}}
\][/tex]
Rewriting the square root as an exponent, we get:
[tex]\[
(x^{24})^{1/2}
\][/tex]
This simplifies to:
[tex]\[
x^{24 \cdot \frac{1}{2}} = x^{12}
\][/tex]
3. Finally, we take the square root of [tex]\(x^{12}\)[/tex]:
[tex]\[
\sqrt{x^{12}}
\][/tex]
Rewriting the square root as an exponent, we get:
[tex]\[
(x^{12})^{1/2}
\][/tex]
This simplifies to:
[tex]\[
x^{12 \cdot \frac{1}{2}} = x^{6}
\][/tex]
Therefore, the expression [tex]\(\sqrt{\sqrt{\sqrt{x^{48}}}}\)[/tex] simplifies to [tex]\(x^6\)[/tex].
So, the correct answer is:
[tex]\[
(A) \, x^6
\][/tex]
