# How do you simplify (root3(9)*root3(6))/(root6(2)*root6(2))?

May 11, 2017

3.

#### Explanation:

$\sqrt[3]{9} = {3}^{\frac{1}{3}} \cdot {3}^{\frac{1}{3}}$
$\sqrt[3]{6} = {2}^{\frac{1}{3}} \cdot {3}^{\frac{1}{3}}$
$\sqrt[6]{2} = {2}^{\frac{1}{6}}$

Now you have $\frac{{3}^{\frac{1}{3}} \cdot {3}^{\frac{1}{3}} \cdot {2}^{\frac{1}{3}} \cdot {3}^{\frac{1}{3}}}{{2}^{\frac{1}{6}} \cdot {2}^{\frac{1}{6}}}$, right?
By Laws of Exponents, you could combine those ${3}^{\frac{1}{3}}$ and ${2}^{\frac{1}{6}}$ and add their bases.

Now you have $3 \cdot {2}^{\frac{1}{3}} / {2}^{\frac{1}{3}}$. Cancelling the fraction part, you'll get 3. :)