Hi kobel51,
When posting questions, you have to be very careful about how you transcribe them; in your post you listed
(1/3)^-3
But I think that you mean...
(1/2)^-3
The "fast way" to answer this question is to realize that the GMAT builds almost all of its questions around patterns. Learning to spot the pattern behind any given question will likely help you to answer it faster.
Here, all of the denominators are "powers of 2" and include negative exponents, so each fraction can be re-written using the same pattern.
(1/2)^-3 = 2^3
(1/4)^-2 = 4^2
(1/16)^-1 = 16^1
Now we can use the "powers of 2" to rewrite the results:
2^3
4^2 = (2^2)^2 = 2^4
(16^1) = 2^4
The question asks us to multiply the fractions, so we have....
(2^3)(2^4)(2^4) = 2^11
We can now take this result and do the "reverse step" to what we did originally...
2^11 = (1/2)^-11
Final Answer: B
GMAT assassins aren't born, they're made,
Rich
