SOLUTION: How do I symplify this equation? (2^-1a^2b)^-3/4a^-9

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Question 152960: How do I symplify this equation?
(2^-1a^2b)^-3/4a^-9
Answer by orca(409) About Me  (Show Source):
You can put this solution on YOUR website!
We need to use the following properties of exponents:
(1)
a%5Em%2Aa%5En=a%5E%28m%2Bn%29
(2)
%28a%5Em%2Ab%5En%29%5Ep+=+a%5E%28mp%29b%5E%28np%29
(3)
a%5E%28-m%29=+1%2Fa%5Em or 1%2Fa%5E%28-m%29=a%5Em
So
%282%5E-1%2Aa%5E2b%29%5E-3%2F4a%5E-9
=
=%282%5E3%2Aa%5E-6%2Ab%5E-3%29%2F%284a%5E-9%29
=8a%5E-6b%5E-3%2Aa%5E9%2F4
=%288%2F4%29a%5E%28-6%2B9%29%2Ab%5E-3
=2a%5E3%2Ab%5E-3
=2a%5E3%2Fb%5E3