ShmoopTube

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And here's your shmoop du jour.

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Which of the following is equivalent to 64 times 1/32 to the 4th times 1/16 to the 5th?

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And here are the potential answers...

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OK, so even if we didn't recognize that each of these numbers is a multiple of 2...

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...we could have glanced at the answer choices and gleaned that fact fast.

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In these kinds of questions we are almost always being asked to convert to powers of

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two... and this question is no exception. So we just convert everything to powers of

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2 and rewrite it.

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It will hurt a bit but the hard work is good for us. Yeah, feel the burn.

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64 is 2 times 2 times 2 times 2 times 2 times 2... or 2 to the 6th.

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32 is 2 to the 5th and 16 is 2 to the 4th.

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The problem now looks like this:

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Note also that when we have exponents in the denominator,

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we can rewrite them as negative numbers...

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...so let's rewrite the problem to account for the fractions.

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Get rid of 'em like they're unwanted body fat...

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and we now have a fully rewritten problem that looks like this:

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First, we multiply the exponents that are being raised to another power like this.

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Once we do that, we can add and subtract the exponents like this...

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...and we get 6 minus 20 minus 20, which is negative 34, and woot, there we go --

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it's answer B. Hope you remembered to stretch first.

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