SOLUTION: If {{{(3x^n)^3 * (3x)^(n-6) = ax^2 }}} what would the values of n and a be?

Algebra ->  Square-cubic-other-roots -> SOLUTION: If {{{(3x^n)^3 * (3x)^(n-6) = ax^2 }}} what would the values of n and a be?      Log On


   

Question 283063: If %283x%5En%29%5E3+%2A+%283x%29%5E%28n-6%29+=+ax%5E2+
what would the values of n and a be?
Found 2 solutions by nabla, MathTherapy:
Answer by nabla(475) About Me  (Show Source):
You can put this solution on YOUR website!
First, simplify the left.

So, we want 2=4n-6.
This implies n=2.
If n=2, a=3^(-1)=1/3.
IE +%281%2F3%29%28x%5E2%29+

Answer by MathTherapy(10898) About Me  (Show Source):
You can put this solution on YOUR website!
If %283x%5En%29%5E3+%2A+%283x%29%5E%28n-6%29+=+ax%5E2+
what would the values of n and a be?
************************************
                   %283x%5En%29%5E3+%2A+%283x%29%5E%28n-6%29+=+ax%5E2
       3%5E3+%2A+%28x%5En%29%5E3+%2A+3%5E%28n+-+6%29+%2A+x%5E%28n+-+6%29+=+ax%5E2
 %283%5E3+%2A+3%5E%28n+-+6%29%29%28x%5E%283n%29+%2A+x%5E%28n+-+6%29%29+=+ax%5E2
     %283%5E%283+%2B+n+-+6%29%29%28x%5E%283n+%2B+n+-+6%29%29+=+ax%5E2
               %283%5E%28n+-+3%29%29%28x%5E%284n+-+6%29%29+=+ax%5E2
                                    x%5E%284n+-+6%29+=+x%5E2 --- Equating terms
                                         4n - 6 = 2 ---- Bases are equal and so are the exponents
                                               4n = 8
                                                highlight%28n+=+8%2F4+=+2%29

                                      3%5E%28n+-+3%29+=+a ---- Equating terms
                                      3%5E%282+-+3%29+=+a ---- Substituting 2 for n
                                        3%5E%28-+1%29+=+a
                                               highlight%281%2F3+=+a%29

You can do the CHECK!!