Question 454170
18 over 3rd root 81
<pre>
{{{18/root(3,81)}}}

Break up 81 this way

81 = 9&#8231;9 = 3&#8231;3&#8231;3&#8231;3 = 3&#8308;

{{{18/root(3,3^4)}}}

To get rid of the 3rd root in the denominator we need 
an exponent of 3 which is a multiple of 3.
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To get that we multiply top and bottom by  &#8731;3²
 

{{{expr(18/root(3,3^4))expr(root(3,3^2)/root(3,3^2))}}}

We multiply tops and bottoms, we multiply under the
radicals on the bottom so we'll have 3&#8310; under the radical
which has an exponent of 6 which is a multiple of 3

{{{18*root(3,3^2)/root(3,3^6)}}}

Now we get rid of the radical on the bottom by
dividing the power of 3 which is 6 by the index of
the root which is 3 and get 3² 


{{{18*root(3,3^2)/3^2}}}

Then we make both 3²'s into 9

{{{18*root(3,9)/9}}}

Then the 9 cancels into the 18 and gives 2 on the top

{{{2*root(3,9)}}}
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So that's the answer 2&#8731;9

Edwin</pre>