Exercise
Simplify the expression:
\frac{\sqrt[3]{a^2}\cdot {(\sqrt[4]{a})}^3}{a\cdot \sqrt[6]{a}}
Final Answer
Solution
Using Powers and Roots rules we get:
\frac{\sqrt[3]{a^2}\cdot {(\sqrt[4]{a})}^3}{a\cdot \sqrt[6]{a}}=
=\frac{a^{\frac{2}{3}}\cdot {(a^{\frac{1}{4}})}^3}{a\cdot a^{\frac{1}{6}}}=
=\frac{a^{\frac{2}{3}}\cdot a^{\frac{3}{4}}}{a^{\frac{7}{6}}}=
=\frac{a^{\frac{17}{12}}}{a^{\frac{7}{6}}}=
=a^{\frac{1}{4}}=
=\sqrt[4]{a}