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

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Answer 1 · 2018-05-11T16:44:36

Answer: $2/9$

Where,
root 4 = $x^(1/4)$
Prime factors of 4 = $2*2$ = $2^2$
Prime factors of 324 = $2*2*3*3*3*3$ = $2^2*3^4$

Now,

= $(2*2^(2*1/4))/(3*2^(2*1/4)*3^(4*1/4)$
= $(2.sqrt(2))/(3.3^1.sqrt(2)$
= $2/3.3$ [ Since $sqrt2$ is cancelled by $sqrt2$ ]
= $2/9$

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