SOLUTION: Where is my mistake? This is the problem (where the image cut off, the power is 1/3): {{{ ( (root( 5, x ) * x^2 * x^(1/3) ) - ( root( 15, x^2 )^2 * x ) ) / root( 15, x^19 ) }}}

Algebra ->  Square-cubic-other-roots -> SOLUTION: Where is my mistake? This is the problem (where the image cut off, the power is 1/3): {{{ ( (root( 5, x ) * x^2 * x^(1/3) ) - ( root( 15, x^2 )^2 * x ) ) / root( 15, x^19 ) }}}      Log On


   

Question 903885: Where is my mistake?
This is the problem (where the image cut off, the power is 1/3):

This is my solution:

Power = 38/15..............Power = -15/15
%28%28x%29%5E%2838%2F15%29%29+-+%28%28x%29%5E%28-15%2F15%29%2A+x%29+
%28x%29%5E%2838%2F15%29-1
The right solution is root%2815%2Cx%5E19%29+-+1
Thanks!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
You're very close. In the numerator, you are really dividing all that mess by root%2815%2Cx%5E19%29

Put another way, you are multiplying the whole numerator by x%5E%28-19%2F15%29%5E%22%22

So you *should* have

[ Numerator ]*( x^(-19/15) )

Meaning that you distribute x^(-19/15) to the two terms inside the numerator. You only multiplied +%28root%28+15%2C+x%5E2+%29%5E2+%2A+x+%29 by x%5E%28-19%2F15%29%5E%22%22,

but forgot to multiply the first term %28root%28+5%2C+x+%29+%2A+x%5E2+%2A+x%5E%281%2F3%29%5E%22%22+%29 by x^(-19/15).

If you do that step, you will get the answer root%2815%2Cx%5E19%29+-+1

Hope that helps. If not, then let me know.