ShmoopTube

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And here's your shmoop du jour...

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Simplify the expression (8) to the -3 times (16) squared.

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And here are the potential answers...

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How in the world do we take a negative exponent?

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The process isn't really that intuitive.

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It's like GIVING someone a bunch of taxes. Just doesn't make natural sense.

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Let's start with the second part of this,

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...square 16... so 16 times 16 which is 256. Done.

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Now we have to figure out how we can negatively cube 8.

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One thing that'll help is to realize that anything to a negative exponent can be rewritten

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as 1 OVER that number...

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...that is, 8 to the negative 3rd power is the same as 1 over just a normal positive 8... cubed.

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So the first part is just 1 over 512.

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Now we have 1 over 512 times 256... which is 256 over 512... or 1 over 2 or just one half.

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And our answer is B.

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