SOLUTION: please solve this using only positive exponents... {{{(3^2) *4^(-4)* b * 3^(-4) *(a^2)* b^(-3)}}}

Algebra ->  Exponents -> SOLUTION: please solve this using only positive exponents... {{{(3^2) *4^(-4)* b * 3^(-4) *(a^2)* b^(-3)}}}      Log On


   

Question 254634: please solve this using only positive exponents...
%283%5E2%29+%2A4%5E%28-4%29%2A+b+%2A+3%5E%28-4%29+%2A%28a%5E2%29%2A+b%5E%28-3%29
Found 2 solutions by drk, richwmiller:
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
Here is the original problem
3%5E2%2A4%5E-4+%2Ab+%2A+3%5E-4+%2Aa%5E2++%2A+b%5E-3
Using positive exponents, we get
%283%5E2%2Ab+%2A+a%5E2%29%2F%284%5E4%2A3%5E4%2Ab%5E3%29
which simplifies to
%28a%5E2%29%2F%284%5E2%2A3%5E2%2Ab%5E2%29
or
%28a%2F%2812b%29%29%5E2

Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
There is nothing to solve since there is no equal sign.
We can simplify it or put it in terms of only positive exponents.
Negative exponents just mean the inverse or reciprocal.
%283%5E2%29+%2A4%5E%28-4%29%2A+b+%2A+3%5E%28-4%29+%2A%28a%5E2%29%2A+b%5E%28-3%29


%283%5E2%29+%2A1%2F4%5E%284%29%2A+b+%2A1%2F+3%5E%284%29+%2A%28a%5E2%29%2A+1%2Fb%5E%283%29
Now you can simplify and cancel
1%2F4%5E%284%29%2A1%2F+3%5E%282%29+%2A%28a%5E2%29%2A+1%2Fb%5E%282%29
a%5E2%2F%2816%5E%282%29%2A+9+%2A+b%5E%282%29%29
a%5E2%2F%282304%2A+b%5E%282%29%29
%28a%2F48b%29%5E2
I am mystified how drk changed the 4^4 to 4^2. I didn't see any cancelling available.