How do you simplify $root5(2)/(3root5(162))$ ?

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Answer 1 · 2017-01-16T07:23:19

$3^-(9/5)$

Given, $root(5)2/[3xx root(5) 162]$

$rArr 2^(1/5)/[3xx(162)^(1/5)]$

$rArr 2^(1/5)/[3xx (2xx81)^(1/5)$

$rArr 2^(1/5)/[3xx2^(1/5)xx(3^4)^(1/5)$

$rArr cancel[2^(1/5)]/[cancel[2^(1/5)] xx3^1 xx 3^(4/5)$

$rArr 1/[3^(1+4/5)$

$rArr 1/[3^{(5+4)/5}]$

$rArr 1/3^(9/5)$

$rArr 3^-(9/5)$

How do you simplify root5(2)/(3root5(162))root5(2)/(3root5(162))?