Lets take the easier Q .
3^180 - 3^30=
How can we solve this thing to get a clean answer. I remember 200% the answer choices were in powers (something like below and not big huge numbers) .
There is no 'simple' way to write 3^180 - 3^30 as a single power. All you can do is factor it; you can first factor out 3^30, then if you want to go further you can use a difference of squares:
3^180 - 3^30 = 3^30 (3^150 - 1) = 3^30 (3^75 + 1)(3^75 - 1)
To factor that any further, you'd need to know some factorization patterns that aren't tested on the GMAT. Notice that by factoring, we aren't making the answer appear any simpler - in fact, it begins to look more complicated.
So if you're '200% sure' that you saw a similar question in which the answer choices were neat powers for a similar question, you'd need to show us the exact question. The only similar question I could imagine where the answers would be simple powers would be something like:
3^180 - 3^30 is closest to
which of the following:
This question is not asking for a simplification at all; it's asking for an estimate. Here you simply need to notice that 3^180 is absolutely enormous in comparison to 3^30, so subtracting 3^30 will barely make any difference at all, and the answer is A.
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