ShmoopTube

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Here’s your shmoop du jour, brought to you by negative integers.

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They’re always preceded by a negative sign. Like…this one.

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If x and y are negative integers, then x to the power of y can be which of the following?

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And here are the potential answers...

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So we have two mystery integers... both negative…

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…and we want to know what happens when we take one to the power of the other.

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Remember, all it takes is ONE working example each of a positive real number, negative real

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number or negative integer to do the trick… Let’s start with A – positive real number.

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Is there an instance where this could happen?

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Well…sure. Any time a negative number is squared, it becomes positive.

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The negative sign in the exponent turns our number into a fraction.

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So… if, for example, x was -1 and y was -2…

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x to the power of y would become 1 over negative 1 squared. Which is just…1. So A works.

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What about a negative real number?

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Sure. If x is -1 and y is -3, the fraction we’d convert that to is 1 over -1 to the 3rd.

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-1 to the 3rd is still negative one… since it gets reflected across the number line twice…

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…and 1 over negative 1 is just negative 1…

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…which is both a negative real number AND a negative integer…

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…meaning that both B and C work as well.

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And if A, B and C are all in the mix…

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…then we’re going to have to go with E as our final answer.

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We hope this video wasn’t a negative experience for you.

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If so, watch it twice and it'll multiply into a positive.

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