SOLUTION: how do i do this? simplify (all positive exponents) {{{(-2rs^-2(3r)^0)/((r^-3s^2)^-2)}}}

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Question 134171: how do i do this?
simplify (all positive exponents)
%28-2rs%5E-2%283r%29%5E0%29%2F%28%28r%5E-3s%5E2%29%5E-2%29
Answer by algebrapro18(249) About Me  (Show Source):
You can put this solution on YOUR website!
simplify (all positive exponents)
%28-2rs%5E-2%283r%29%5E0%29%2F%28%28r%5E-3s%5E2%29%5E-2%29
first off you need to know a few simple rules

1. Any Quantity to the 0 power simplifies down to 1
2. Any Quantity to the - power gets reciprocated.
ex) x%5E-1+=+1%2Fx
3. To multiply two quantities raised to powers you add the powers

so using these rules and taking things one step at a time

%28-2rs%5E-2%283r%29%5E0%29%2F%28%28r%5E-3s%5E2%29%5E-2%29 --> Simplifying the quantity to the 0 power
=+%28-2rs%5E-2%29%2F%28%28r%5E-3s%5E2%29%5E-2%29 --> Simplify the negative external powers
=+%28-2r%28r%5E-3s%5E2%29%5E2%29%2F%28s%5E2%29 --> Squaring r^-3s^2
=+%28-2r%28r%5E-6s%5E4%29%29%2F%28s%5E2%29 --> Multiply through by -2r
=+%28-2r%5E-5s%5E4%29%2F%28s%5E2%29 --> dividing by s^2
=+-2r%5E-5s%5E2 --> Writing with positive exponents
=+%28-2s%5E2%29%2Fr%5E5