SOLUTION: Chapter covers: Properties of Integral Exponents Problem: It says to simplify each exponential expression. () top & bottom half all in one parethesis

You either mean this:

9y4     (x-1)-2
———— + —————————
x-2       y2

or this:

9y4 + (x-1)-2
—————————————
   x-2y2 

I'll do both:

In either case, you must learn the rule for getting 
rid of negative exponents.

If a numerator (respectively, denominator) either is 
or has a factor which is an exponential with a 
negative exponent, then move the base and exponent 
to the denominator (respectively, to the numerator)
and change the sign of the exponent to positive.

If it's this way:

9y4     (x-1)-2
———— + —————————
x-2       y2

  
In the first fraction, move the x-2 from the 
denominator to the numerator and change the sign of
the -2 exponent to +2 and write x2 in the numerator, 
and put a 1 in the denominator:

9y4x2     (x-1)-2
————— + —————————
  1         y2

In the second fraction multiply the outer exponent 
-2 by the inner exponent -1, getting +2 so it ends
up having a positive exponent, and there is no 
negative exponent to get rid of:

In the first fraction, move the x-2 from the 
denominator to the numerator and change the sign of 
the -2 exponent to +2 and write x2 in the numerator, 
and put a 1 in the denominator:

9y4x2    x2
————— + ———
  1      y2

Now the LCD is y2, so to make the first fraction 
have this LCD for its denominator, multiply top 
and bottom by y2

9y4x2·y2    x2
———————— + ———
  1·y2      y2 

Add the exponents of y in the numerator of the 
first fraction, and eliminate the "1·" in the bottom

9y6x2    x2
————— + ———
  y2     y2

Add the numerators and place over the common 
denominator

9y6x2 + x2
——————————
     y2     

You may not do any canceling here.  You can, however, 
factor out an x2 from the numerator, if you like:

x2(9y6 + 1)
——————————
    y2

=====================================
 
If you meant this:

9y4 + (x-1)-2
—————————————
   x-2y2 

Then In the second term on top, multiply the outer
exponent -2 by the inner exponent -1 getting +2 so 
it ends up having a positive exponent, and there is
no negative exponent to get rid of:

9y4 + x2
————————
  x-2y2

Now x-2 is a factor of the denominator, so move it 
from denominator to numerator by changing the sign 
of the -2 exponent and writing it in the top as x2.
However it must be a FACTOR of the numerator, so the
two terms in the numerator must by enclosed in 
parentheses:

x2(9y4 + x2)
————————————
    y2

This is as far as you can go.

Edwin
AnlytcPhil@aol.com