Questions on Algebra: Equations answered by real tutors!

(1)  First, 8.3% wrong solutions is too much for an AI.
     You may say "ok, in 20 years it will be perfect".
     Probably, it can be true, but I tell you about what I see now.

     By the way, my feeling is that good AI acceptable level for wrong solutions
     should be at most 1:1000, or 0.1%.



(2)  Second, it can be perfect in 20 years under one necessary condition: 
     the best minds in Math solving, writing and teaching, the best Math educators  
     and the best computer programming specialists will work on it 
     starting from now and during 20 years.


     What does it mean and why ? - Raising and educating a specialist in solving Math, writing Math 
     and explaining Math takes 10 - 15 - 20 years to get a professional level, when a person can speak, 
     write and teach professionally. (And, usually, the fingers of one hand are enough 
     to count such specialists of a national level in each country and in each generation).


     If you make such experiments with the novices, it will take 10-15-20 years for them to get a professional 
     level before they will learn to speak/write at the professional level, so it is a WRONG way to assign 
     novices for key positions for such an activity.


     It is the second conclusion from my arguments: the writers and the content creators must be professionals
     from the very beginning. Neither @mananth, nor @CPhill are such professionals.



(3)  Third, when a computer code (like Artificial Intelligence) produces wrong solutions, it becomes 
     double and triple dangerous, since it works as the source of unlimited erroneous solutions.

     So, such pretendent to the AI position is needed in doubled and tripled attention from developers,
     from well-wishers around and from the whole community.



     Often, I see the solutions by @mananth (= or his code) that produce correct final answer,
     but are incorrect from the point of view of the teaching methodology.

     When a computer code (like Artificial Intelligence) produces pedagogically wrong solutions, 
     then such tools become inappropriate for teaching - and again, they require doubled and tripled attention.



(4)  Fourth, the computer codes which I see in the posts by @CPhill or @mananth, have no that level of flexibility
     and precision to serve at the adequate level.  So, the level of the computer coders must be at least 
     one order (one level) higher.



(5)  Fifth, the writing, coding and programming discipline must be changed.

     For now, the AI codes for solving school Math problems that I saw so far, do not show a tendency 
     to make checks of their solutions. They do not think that is is MANDATORY.  It is a crude error, 
     which must be fixed.



(6)  Next.  As the life has taught me, many of incoming problems are mathematically non-sensical.
     So, the input flow is quite dirty, and therefore, idiotic incoming problems should be filtered out.

Hi, I was wondering if someone could help me. I have no idea how to complete this problem, and I need to 
show my work (steps). So, if anyone has any help they can provide, I would greatly appreciate it. Thank you. 

Simplify

cubrt(27x^4y^10).

Explain your answer and show all steps. 
=======================================

   

Any line parallel to  2x = 9y + 8  has the form

    2x = 9y + c,    (1)

where 'c' is a real constant.  To find 'c', we simply insert coordinates (-6,7) into equation (1)

    2*(-6) = 9*7 + c,

    -12 - 63 = c,

    c = -75.


Thus equation (1) takes the form

    2x = 9y - 75.    (2)


To get the form  y = mx + b, we express 'y' from equation (2)

    y =  + ,

or,  which is the same

    y =  + 8.    (3)


So, the slope of the sough line is  m =   and its equation is  y =  + 8.

First find the slope of the line  

    m =  =  =  = .


Notice that    is not -0.33,  as @mananth mistakenly states and uses.


Plug the value of the slope and the values of the coordinates (-7,-9) of the given point  
in the point-slope equation of the line 

    y = mx + b,

    -9 =  + b,

    b = -9 +  =  =  = -6.


So, an equation is

    y =  - 6.


It is the slope-intercept form equation.


Notice that it is absolutely different from that in the post by @mananth.