SOLUTION: 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

Question 243853: cube root of 27w to the 12th power over 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
Found 2 solutions by scott8148, MathTherapy:
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
breaking the denominator into sums is NOT a good technique for simplifying this

my two cents:

multiplying the fraction by 10/10 ___ cbrt[(10 * 27w^12) / 1000]

extracting WHOLE roots ___ (3w^4 / 10)cbrt(10)

this leaves no roots in the denominator
Answer by MathTherapy(10557) (Show Source): You can put this solution on YOUR website!

cube root of 27w to the 12th power over 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 Neither, I'm afraid to say!! One error I noticed: . Plus, the denominator cannot be split the way you two did! ----- Multiplying RADICAND by 1: = = OR = = = , or

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