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Powers and Roots – Simplify an expression with powers – Exercise 5570

Exercise

Simplify the expression:

\frac{\sqrt[3]{a^2}\cdot {(\sqrt[4]{a})}^3}{a\cdot \sqrt[6]{a}}

Final Answer

\frac{\sqrt[3]{a^2}\cdot {(\sqrt[4]{a})}^3}{a\cdot \sqrt[6]{a}}=\sqrt[4]{a}

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}

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