Question 243853
<pre>
cube root of 27w to the 12th power over 100

{{{cube( 27w^12/100 ) }}}

Explanation:

I am a volunteer math tutor.  My student disagrees with the answer I came up with, so I am writing to you for any help in
justifying her answer or my answer as "more correct".  Here's the problem:  Show your work in solving this cube root problem.

The heart of the question is my student's answer vs. my answer.  Which one is more correct?

Student:
cube( (3 x 3 x 3) w^(4 x 3)/(75 + 25) )
 3w4/(5 x 5 x 5) + cube( 25 )
 3w4/5 + cube ( 25 ) <<< student's answer

Tutor:
cube( (3 x 3 x 3) w^(4 x 3)/(75 + 17 + 8) )
 3w4/(5 x 5 x 5) + cube( 17 ) + (2 x 2 x 2)
 3w4/5 + cube ( 17 ) + 2
 3w4/7 + cube (17) <<< tutor's answer

Which answer will the teacher of my student consider as "correct" ?

 3w4/5 + cube ( 25 ) OR 3w4/7 + cube (17)

Thank you.  Rob Miller

<font color = red><font size = 4><b>Neither, I'm afraid to say!! One error I noticed: {{{5x5x5 <> 75}}}</font></font></b>.
Plus, the denominator cannot be split the way you two did!

{{{root (3, (27w^12)/100)}}} 
{{{root (3, (10/10)((27w^12)/(100)))}}} ----- Multiplying RADICAND by 1: {{{10/10}}}
{{{root (3, 10(3w^4)^3/10^3)}}} = {{{(3w^4/10)root (3, 10/1)}}} = {{{highlight((3w^4/10)(root (3, 10)))}}}

OR

{{{root (3, (27w^12)/100)}}} = {{{root (3, (3w^4)^3/100)}}} = {{{(3w^4)*root(3, (1/100))}}} = {{{highlight((3w^4)*root(3, 10^(- 2))))}}}, or {{{highlight((3w^4)*matrix(2,1, " ", (10^(- 2/3)))))}}}</pre>