Rút gọn biểu thức: P = căn bậc hai a (căn bậc hai a (căn bậc hai a (căn bậc hai a
Câu hỏi:
Rút gọn biểu thức: \(P = \sqrt {a\sqrt {a\sqrt {a\sqrt a } } } :{a^{\frac{{11}}{{16}}}}\).
Trả lời:
\(P = \sqrt {a\sqrt {a\sqrt {a\sqrt a } } } :{a^{\frac{{11}}{{16}}}}\)
\[ = {\left\{ {a{{\left[ {a{{\left( {a\,.\,{a^{\frac{1}{2}}}} \right)}^{\frac{1}{2}}}} \right]}^{\frac{1}{2}}}} \right\}^{\frac{1}{2}}}:{a^{\frac{{11}}{{16}}}} = {\left\{ {a{{\left[ {a{{\left( {{a^{\frac{3}{2}}}} \right)}^{\frac{1}{2}}}} \right]}^{\frac{1}{2}}}} \right\}^{\frac{1}{2}}}:{a^{\frac{{11}}{{16}}}}\]
\[ = {\left[ {a{{\left( {a\,.\,{a^{\frac{3}{4}}}} \right)}^{\frac{1}{2}}}} \right]^{\frac{1}{2}}}:{a^{\frac{{11}}{{16}}}} = {\left[ {a{{\left( {{a^{\frac{7}{4}}}} \right)}^{\frac{1}{2}}}} \right]^{\frac{1}{2}}}:{a^{\frac{{11}}{{16}}}}\]
\[ = {\left( {a\,.\,{a^{\frac{7}{8}}}} \right)^{\frac{1}{2}}}:{a^{\frac{{11}}{{16}}}} = {\left( {{a^{\frac{{15}}{8}}}} \right)^{\frac{1}{2}}}:{a^{\frac{{11}}{{16}}}}\]
\[ = {a^{\frac{{15}}{{16}}}}:{a^{\frac{{11}}{{16}}}} = {a^{\frac{{15}}{{16}} - \frac{{11}}{{16}}}} = {a^{\frac{1}{4}}}\]
