SOLUTION: I need help solving for x: ((3x^2)^-1(3x^5)^-2)/(3^-1*x^-2)^3

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Question 753563: I need help solving for x: ((3x^2)^-1(3x^5)^-2)/(3^-1*x^-2)^3
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
We cannot "solve that for x" because it is not an equation.
Equations always contain the equal sign " = " but what we have
above does not contain an equal sign.  Could there be a typo?
Maybe not.  Perhaps instead the instructions was "simplify the 
expression, leaving final answer with only positive exponents".
If so, then:

%28%283x%5E2%29%5E%28-1%29%283x%5E5%29%5E%28-2%29%29%2F%283%5E%28-1%29%2Ax%5E%28-2%29%29%5E3

Give every factor inside parentheses an exponent.
If it doesn't have one, give it a 1 exponent:



To remove the parentheses, multiply every exponent
which is inside a set of parentheses by the exponent outside
the parentheses on the right:

%283%5E%28-1%29x%5E%28-2%293%5E%28-2%29x%5E%28-10%29%29%2F%283%5E%28-3%29%2Ax%5E%28-6%29%29

Get rid of all the negative exponents by moving the factors
from the numerator to the denominator or denominator to the
numerator and changing the sign of the exponent to positive:



I just put those +'s in there for emphasis

%283%5E3%2Ax%5E6%29%2F%283%5E1x%5E2%2A3%5E2x%5E10%29

In the bottom, add the exponents of the 3's and 
add the exponents of the x's:

%283%5E3x%5E6%29%2F%283%5E3%2Ax%5E12%29

Cancel the 33's

%28cross%283%5E3%29x%5E12%29%2F%28cross%283%5E3%29%2Ax%5E6%29

x%5E6%2Fx%5E12 

Subtract the exponents of the x's, larger minus smaller,
12-6=6, and since the larger exponent 12 was on the bottom, we
put the resulting x%5E6 on the bottom, which means we have
to put a "1" for the numerator:

1%2Fx%5E6

Edwin