Question

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

Answer 1

Answer: `2/9`

Explanation:

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`