SOLUTION: Pls assist in solving:{{{ 16x^(-3) = 2x^(-6) }}}

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Question 944238: Pls assist in solving:+16x%5E%28-3%29+=+2x%5E%28-6%29+
Found 2 solutions by harpazo, Edwin McCravy:
Answer by harpazo(655) About Me  (Show Source):
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
The other tutor's answer above is incorrect.  The other tutor gave the
solution for +%2816x%29%5E%28-3%29+=+%282x%29%5E%28-6%29+.  The 2 and the 16 are not in
parentheses so they are not raised to those negative powers.  Only x is
raised to those negative powers in your equation.

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+16x%5E%28-3%29+=+2x%5E%28-6%29+

Divide both sides by 2

+8x%5E%28-3%29+=+x%5E%28-6%29+

Write the factors with negative exponents as denominator
factors with positive exponents:

+8%2Fx%5E3+=+1%2Fx%5E6+

Cross-multiply:

8x%5E6=x%5E3

Get 0 on the right sides:

8x%5E6-x%5E3=0

Factor out x³

x%5E3%288x%5E3-1%29=0

x%5E3=0,  8x%5E3-1=0

x=0,    %282x%29%5E3-1%5E3=0

0 is not a solution because 0 may only be raised to 
positive powers, and the original has negative powers.
The second equation requires the factorization of the
difference of two cubes:


              %282x-1%29%28%282x%29%5E2%2B2x%2A1%2B1%5E2%29

              %282x-1%29%284x%5E2%2B2x%2B1%29

              2x-1=0   4x%5E2%2B2x%2B1=0

              2x=1     x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
             
              x=1%2F2    x+=+%28-2+%2B-+sqrt%28+2%5E2-4%2A4%2A1+%29%29%2F%282%2A4%29+

                             x+=+%28-2+%2B-+sqrt%284-16+%29%29%2F8+

                             x+=+%28-2+%2B-+sqrt%28-12+%29%29%2F8+

                             x+=+%28-2+%2B-+i%2Asqrt%2812+%29%29%2F8+

                             x+=+%28-2+%2B-+i%2Asqrt%284%2A3+%29%29%2F8+

                             x+=+%28-2+%2B-+2i%2Asqrt%283+%29%29%2F8+

                             x+=+%282%28-1+%2B-+i%2Asqrt%283+%29%29%29%2F8+

                             x+=+%28-1+%2B-+i%2Asqrt%283%29%29%2F4

So there are three solutions 1%2F2, %28-1+%2B+i%2Asqrt%283%29%29%2F4, %28-1+-+i%2Asqrt%283%29%29%2F4  


Edwin