# How do you divide \frac { 2\root[ 4] { 4} } { 3\root [ 4] { 324} }?

May 11, 2018

Answer: $\frac{2}{9}$

#### Explanation:

Where,
root 4 = ${x}^{\frac{1}{4}}$
Prime factors of 4 = $2 \cdot 2$ = ${2}^{2}$
Prime factors of 324 = $2 \cdot 2 \cdot 3 \cdot 3 \cdot 3 \cdot 3$ = ${2}^{2} \cdot {3}^{4}$

Now,

= (2*2^(2*1/4))/(3*2^(2*1/4)*3^(4*1/4)
= (2.sqrt(2))/(3.3^1.sqrt(2)
= $\frac{2}{3.3}$ [ Since $\sqrt{2}$ is cancelled by $\sqrt{2}$ ]
= $\frac{2}{9}$