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Here’s an unshmoopy question you’ll find on the exam…
Which of the following is equivalent to 64 times 1/32 to the 4th times 1/16 to the 5th?
And here are the potential answers: OK, so even if we didn’t recognize that
each of these numbers is a multiple of 2…
…we could have glanced at the answer choices and gleaned that fact fast.
In these kinds of questions we are almost always being asked to convert to powers of
two… and this question is no exception. So we just convert everything to powers of
2 and rewrite it.
It will hurt a bit but the hard work is good for us. Yeah, feel the burn.
64 is 2 times 2 times 2 times 2 times 2 times 2… or 2 to the 6th.
32 is 2 to the 5th and 16 is 2 to the 4th.
The problem now looks like this:
Note also that when we have exponents in the denominator, we can rewrite them as negative
numbers…
…so let’s rewrite the problem to account for the fractions.
Get rid of ‘em like they’re unwanted body fat… and we now have a fully rewritten problem
that looks like this:
Thank you, Curves. Now all we have to do is add and subtract
the exponents… …yeah – remember that rule…
…and we get 6 minus 20 minus 20, which is negative 34, and woot, there we go – it’s
answer B. Hope you remembered to stretch first.