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

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Solution

Using Powers and Roots rules we get:

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

$=\frac{a^{\frac{2}{3}}\cdot {(a^{\frac{1}{4}})}^3}{a\cdot a^{\frac{1}{6}}}=$

$=\frac{a^{\frac{2}{3}}\cdot a^{\frac{3}{4}}}{a^{\frac{7}{6}}}=$

$=\frac{a^{\frac{17}{12}}}{a^{\frac{7}{6}}}=$

$=a^{\frac{1}{4}}=$

$=\sqrt[4]{a}$