Question

Giúp em với ạ!!!

Answer 1

20.

\(F=\dfrac{a^{\dfrac{2}{3}}\left(a^{-\dfrac{2}{3}}-a^{\dfrac{1}{3}}\right)}{a^{\dfrac{1}{8}}\left(a^{\dfrac{3}{8}}-a^{-\dfrac{1}{8}}\right)}=\dfrac{a^{\dfrac{2}{3}-\dfrac{2}{3}}-a^{\dfrac{2}{3}+\dfrac{1}{3}}}{a^{\dfrac{1}{8}+\dfrac{3}{8}}-a^{\dfrac{1}{8}-\dfrac{1}{8}}}=\dfrac{a^0-a}{a^{\dfrac{1}{2}}-a^0}=\dfrac{1-a}{\sqrt{a}-1}=-1-\sqrt{a}\)

\(\Rightarrow F=-1-2017^{1009}\)

21.

\(K=\sqrt[3]{\dfrac{2}{3}\sqrt[3]{\dfrac{2}{3}.\left(\dfrac{2}{3}\right)^{\dfrac{1}{2}}}}=\sqrt[3]{\dfrac{2}{3}\sqrt[3]{\dfrac{2}{3}^{\dfrac{3}{2}}}}=\sqrt[3]{\dfrac{2}{3}.\left(\dfrac{2}{3}\right)^{\dfrac{1}{2}}}\)

\(=\sqrt[3]{\left(\dfrac{2}{3}\right)^{\dfrac{3}{2}}}=\left(\dfrac{2}{3}\right)^{\dfrac{1}{2}}\)

22.

\(\sqrt[]{x\sqrt[]{x\sqrt[]{x.x^{\dfrac{1}{2}}}}}=\sqrt[]{x\sqrt[]{x\sqrt[]{x^{\dfrac{3}{2}}}}}=\sqrt[]{x\sqrt[]{x.x^{\dfrac{3}{4}}}}=\sqrt[]{x\sqrt[]{x^{\dfrac{7}{4}}}}=\sqrt[]{x.x^{\dfrac{7}{8}}}\)

\(=\sqrt[]{x^{\dfrac{15}{8}}}=x^{\dfrac{15}{16}}\)

\(x^{\dfrac{15}{16}}:x^{\dfrac{11}{16}}=x^{\dfrac{4}{16}}=x^{\dfrac{1}{4}}=\sqrt[4]{x}\)

23.

A đúng, do \(a^{\sqrt[]{3}}< a^{\sqrt[]{5}}\Rightarrow\dfrac{1}{a^{\sqrt[]{3}}}>\dfrac{1}{a^{\sqrt[]{5}}}\)

24.

A đúng