SOLUTION: 2x^-3/6x^-3 i have to simplify. i have used a^b/a^c=a^b-c.. but i cant get the answer x/3 i tried reducing the fraction x^-3/3x^-4 but know where to go from there

Oh I get it.  There was a typo in your first statement of the 
expression. There was supposed to be a -4 exponent on the bottom, 
not the way you gave it at first with a -3 exponent on the bottom.

     

The best way to handle factors of numerators and denominators
with negative exponents in a fraction is to change the
expression so that it will have only positive exponents by this
procedure:

Move the factor with the negative exponent across the 
fraction bar and change the sign of the negative 
exponent to positive.

By "move the factor across the fraction bar", I mean that if the 
factor with the negative exponent is in the numerator, move it 
to the denominator and change the sign of the exponent.  And 
vice-versa, if the factor with the negative exponent is in the 
denominator, move it to the  numerator and change the sign of 
the exponent.

     

There are factors in both numerator and denominator with
negative exponents.  Therefore move the x-3 from
the numerator to the denominator and change the sign of the
exponent so that you have x3 in the denominator.

Also in the same step, move the x-4 from
the denominator to the numerator and change the sign of the
exponent so that you have x4 in the numerator.
denominator as 

     

Then subtract exponents of x:  4-3 = 1

     

or just

     

and then divide top and bottom by 2

     

Edwin

Oh I get it.  There was a typo in your first statement of the 
expression. There was supposed to be a -4 exponent on the bottom, 
not the way you gave it at first with a -3 exponent on the bottom.

     

The best way to handle factors of numerators and denominators
with negative exponents in a fraction is to change the
expression so that it will have only positive exponents by this
procedure:

Move the factor with the negative exponent across the 
fraction bar and change the sign of the negative 
exponent to positive.

By "move the factor across the fraction bar", I mean that if the 
factor with the negative exponent is in the numerator, move it 
to the denominator and change the sign of the exponent.  And 
vice-versa, if the factor with the negative exponent is in the 
denominator, move it to the  numerator and change the sign of 
the exponent.

     

There are factors in both numerator and denominator with
negative exponents.  Therefore move the x-3 from
the numerator to the denominator and change the sign of the
exponent so that you have x3 in the denominator.

Also in the same step, move the x-4 from
the denominator to the numerator and change the sign of the
exponent so that you have x4 in the numerator.
denominator as 

     

Then subtract exponents of x:  4-3 = 1

     

or just

     

and then divide top and bottom by 2

     

Edwin