Viết mỗi biểu thức sau dưới dạng một lũy thừa (a > 0):

a) $\sqrt[4]{2^{-3}}$ ;

b) $\frac{1}{\sqrt[5]{2^3}}$ ;

c) ${\left(\sqrt[5]{3}\right)}^4$ ;

d) $\sqrt{a\sqrt[3]{a}}$;

e) $\sqrt[3]{a}.\sqrt[4]{a^3}:{\left(\sqrt[6]{a}\right)}^5$ ;

g) $a^{\frac{1}{3}}:a^{-\frac{3}{2}}.a^{-\frac{2}{3}}$ .

a) $\sqrt[4]{2^{-3}}=\sqrt[4]{{\left(\frac{1}{2}\right)}^3}={\left(\frac{1}{2}\right)}^{\frac{3}{4}}=2^{-\frac{3}{4}}$

b) $\frac{1}{\sqrt[5]{2^3}}=\frac{1}{2^{\frac{3}{5}}}={\left(\frac{1}{2}\right)}^{\frac{3}{5}}=2^{-\frac{3}{5}}$

c) ${\left(\sqrt[5]{3}\right)}^4=\sqrt[5]{3^4}=3^{\frac{4}{5}}$

d) $\sqrt{a\sqrt[3]{a}}=\sqrt{{\left(\sqrt[3]{a}\right)}^3.\sqrt[3]{a}}=\sqrt{{\left(\sqrt[3]{a}\right)}^4}=\sqrt{\sqrt[3]{a^4}}=\sqrt[3]{a^2}=a^{\frac{2}{3}}$

e) $\sqrt[3]{a}.\sqrt[4]{a^3}:{\left(\sqrt[6]{a}\right)}^5=a^{\frac{1}{3}}.a^{\frac{3}{4}}:a^{\frac{5}{6}}=a^{\frac{1}{3}+\frac{3}{4}-\frac{5}{6}}=a^{\frac{1}{4}}$

g) $a^{\frac{1}{3}}:a^{-\frac{3}{2}}.a^{-\frac{2}{3}}=a^{\frac{1}{3}-\left(-\frac{3}{2}\right)+\left(-\frac{2}{3}\right)}=a^{\frac{1}{3}+\frac{3}{2}-\frac{2}{3}}=a^{\frac{7}{6}}$