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

Exercise

Simplify the expression:

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

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

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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