SOLUTION: how do i simplify this without using zero or negative integers as exponents? {ab^2c^-2}^-3

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Question 404628: how do i simplify this without using zero or negative integers as exponents?
{ab^2c^-2}^-3
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
%28a%2Ab%5E2%2Ac%5E%28-2%29%29%5E%28-3%29
With these problems I like to simplify first. Sometimes the process of simplification causes the zero and/or negative exponents to disappear on their own. After simplifying, if there are still zero or negative exponents, then handle that at the end.

So we'll start with simplifying. The rule for exponents for this type of expression is %28p%2Aq%29%5Ez+=+p%5Ez%2Aq%5Ez
Applying this rule to your expression we get:
%28a%29%5E%28-3%29%2A%28b%5E2%29%5E%28-3%29%2A%28c%5E%28-2%29%29%5E%28-3%29
The rule for a power of a power is to multiply the exponents:
%28a%29%5E%28-3%29%2A%28b%5E%282%2A%28-3%29%29%29%2A%28c%5E%28%28-2%29%2A%28-3%29%29%29
which simplifies to:
a%5E%28-3%29%2Ab%5E%28-6%29%2Ac%5E6
We're done simplifying. Now we'll address the negative exponents that remain. In general p%5E%28-n%29+=+1%2Fp%5En. Using this pattern on the negative exponents in your expression we get:
%281%2Fa%5E3%29%2A%281%2Fb%5E6%29%2Ac%5E6
which simplifies to:
c%5E6%2F%28a%5E3%2Ab%5E6%29