Đáp án:${x^{\frac{{255}}{{256}}}}$
Giải thích các bước giải:
$\begin{array}{l}
\sqrt {x\sqrt {x\sqrt {x\sqrt {x\sqrt {x\sqrt {x\sqrt {x\sqrt x } } } } } } } \\
= \sqrt {x\sqrt {x\sqrt {x\sqrt {x\sqrt {x\sqrt {x\sqrt {x.{x^{\frac{1}{2}}}} } } } } } } \\
= \sqrt {x\sqrt {x\sqrt {x\sqrt {x\sqrt {x\sqrt {x\sqrt {{x^{\frac{3}{2}}}} } } } } } } \\
= \sqrt {x\sqrt {x\sqrt {x\sqrt {x\sqrt {x\sqrt {x.{x^{\frac{3}{4}}}} } } } } } \\
= \sqrt {x\sqrt {x\sqrt {x\sqrt {x\sqrt {x\sqrt {{x^{\frac{7}{4}}}} } } } } } \\
= \sqrt {x\sqrt {x\sqrt {x\sqrt {x\sqrt {x.{x^{\frac{7}{8}}}} } } } } \\
= \sqrt {x\sqrt {x\sqrt {x\sqrt {x\sqrt {{x^{\frac{{15}}{8}}}} } } } } = \sqrt {x\sqrt {x\sqrt {x\sqrt {x.{x^{\frac{{15}}{{16}}}}} } } } \\
= \sqrt {x\sqrt {x\sqrt {x\sqrt {{x^{\frac{{31}}{{16}}}}} } } } = \sqrt {x\sqrt {x\sqrt {x.{x^{\frac{{31}}{{32}}}}} } } = \sqrt {x\sqrt {x\sqrt {{x^{\frac{{63}}{{32}}}}} } } \\
= \sqrt {x\sqrt {x.{x^{\frac{{63}}{{64}}}}} } = \sqrt {x.{x^{\frac{{127}}{{128}}}}} = \sqrt {{x^{\frac{{255}}{{128}}}}} = {x^{\frac{{255}}{{256}}}}
\end{array}$
