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

1 Answer
APIL C.
May 11, 2018

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#

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