Question 256746
the fifth root of 27 to the third power 
<pre><font size = 4 color = "indigo"><b>

Do you mean this:

{{{(root(5,27))^3}}}

or this

{{{root(5,(27^3))}}}

Whichever way you meant they work out to have
the same value.

They also have the same value as 

{{{drawing(50,50,0,3,-.5,1.5,locate(0,1,27^(3/5)))}}}

What did you want to do with it? You didn't say.
If the instructions are to write it with a fractional
exponent the preceding is the answer.  If they said
to approximate it with a decimal then the answer is
7.224674056

If they told you to write it in simplest radical form
with smallest possible base, then

{{{(root(5,(27)))^3}}}

{{{drawing(50,50,0,3,-.5,1.5,locate(0,1,27^(3/5)) )}}}

{{{(3^3)^(3/5)}}}

{{{drawing(50,50,0,3,-.5,1.5,locate(0,1,3^(9/5) ) )}}}

{{{root(5,(3^9))}}}

{{{root(5,(3^(5+4)))

{{{root(5,3^5*3^4}}}

{{{root(5,(3^5))root(5,(3^4))}}}

{{{3*root(5,(3^4))}}}

Always state what the instructions are for the problem because
often there are many different things you could be asked to
do with the same expression or equation.

Edwin</pre>