Question

Viết các biểu thức sau dưới dạng một luỹ thừa \(\left( {a > 0} \right)\):

a) \(3.\sqrt 3 .\sqrt[4]{3}.\sqrt[8]{3}\);

b) \(\sqrt {a\sqrt {a\sqrt a } } \);

c) \(\frac{{\sqrt a .\sqrt[3]{a}.\sqrt[4]{a}}}{{{{\left( {\sqrt[5]{a}} \right)}^3}.{a^{\frac{2}{5}}}}}\).

Answer 1

a: \(=3\cdot3^{\dfrac{1}{2}}\cdot3^{\dfrac{1}{.4}}\cdot3^{\dfrac{1}{8}}=3^{1+\dfrac{1}{2}+\dfrac{1}{4}+\dfrac{1}{8}}=3^{\dfrac{15}{16}}\)

b: \(=\sqrt{a\cdot\sqrt{a\cdot a^{\dfrac{1}{2}}}}\)

\(=\sqrt{a\cdot\sqrt{a^{\dfrac{3}{2}}}}=\sqrt{a\cdot a^{\dfrac{3}{4}}}=\sqrt{a^{\dfrac{7}{4}}}=a^{\dfrac{7}{4}\cdot\dfrac{1.}{2}}=a^{\dfrac{7}{8}}\)

c: \(=\dfrac{a^{\dfrac{1}{2}}\cdot a^{\dfrac{1}{3}}\cdot a^{\dfrac{1}{4}}}{\left(a^{\dfrac{1}{5}}\right)^3\cdot a^{\dfrac{2}{5}}}=\dfrac{a^{\dfrac{13}{12}}}{a}=a^{\dfrac{1}{12}}\)