SOLUTION: Simplify, leaving only positive exponents in final answer: {{{(p^2qr^3)/(4p^(-1)q^2r^(-1))^2}}}

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Simplify, leaving only positive exponents in final answer: {{{(p^2qr^3)/(4p^(-1)q^2r^(-1))^2}}}      Log On


   



Question 334803: Simplify, leaving only positive exponents in final answer:
%28p%5E2qr%5E3%29%2F%284p%5E%28-1%29q%5E2r%5E%28-1%29%29%5E2

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
%28p%5E2qr%5E3%29%2F%284p%5E%28-1%29q%5E2r%5E%28-1%29%29%5E2

To remove the parentheses, first make sure every factor
inside the parentheses has its exponents showing, so we'll
even put a 1 exponent for the 4, since it's a factor inside
the parentheses:
%28p%5E2qr%5E3%29%2F%284%5E1p%5E%28-1%29q%5E2r%5E%28-1%29%29%5E2
Remove the parentheses on the bottom by multiplying every
exponent inside the parentheses by the exponent outside the
parentheses:

%28p%5E2qr%5E3%29%2F%284%5E2p%5E%28-2%29q%5E4r%5E%28-2%29%29
Get rid of the negative exponents (in red)
%28p%5E2qr%5E3%29%2F%284%5E2p%5E%28red%28-2%29%29q%5E4r%5E%28red%28-2%29%29%29
by moving the factors from the bottom to the top and
changing the sign of their exponents to positive:
%28p%5E2qr%5E3p%5Ered%282%29r%5Ered%282%29%29%2F%284%5E2q%5E4%29
Now we
1. add the exponents of p in the top 2%2B2=4
2. add the exponents of r in the top 3%2B2=5
3. do the exponent 4%5E2=16
%28p%5E4qr%5E5%29%2F%2816q%5E4%29
Give the q in the top the exponent 1:
%28p%5E4q%5E1r%5E5%29%2F%2816q%5E4%29
Subtract the exponents of q, larger minus smaller, getting 4-1+=+3
putting the result q%5E3 in the bottom because the larger exponent
4 was in the bottom. (Eliminate q from the top, of course)
%28p%5E4r%5E5%29%2F%2816q%5E3%29
That's as far as it will simplify.
Edwin