ShmoopTube

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Powers, a la Shmoop.

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Sometimes, the greatest power comes in the smallest packages. [Gift box opens and glove punches girl in the face]

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Take David for example. Goliath never knew what hit him.

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How about Napoleon? He certainly didn’t win any battles because of his height.

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There’s a reason we have something in math called a “power.” [Teacher discussing powers]

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It’s small and unassuming…but it packs quite a punch.

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Also referred to as an “exponent,” a power is a way of abbreviating very large numbers

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in order to make them manageable. See that itty-bitty number, up and to the [Arrow points to a 3 exponent]

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right of the other number? That guy’s the exponent.

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An exponent can take an expression like 5 times 5 times 5 times 5, and express it this way:

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We’re multiplying four 5’s together, so our exponent is a 4.

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Or, as we might say, we are taking “5 to the fourth power.”

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Sometimes you’ll have a bunch more numbers to multiply together than just four of ‘em.

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But life’s too precious to waste it multiplying zillions of numbers the long way…hence the shortcut. [Lots of numbers as girl takes shortcut]

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What about when the power is 1? Because our exponent is telling us that there

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is only one seven, he doesn’t get multiplied by anything else.

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So it’s the same as plain ol’ seven. When a power is zero, however, the number

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is always equal to one. [Teacher drawing 7 to the power of 0]

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Which…really is the loneliest number. We’ve been there. [Man sat waiting at a table]

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Moving on…an exponent can also be negative.

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In that case, you’ll need to take the reciprocal of the number…[Young boy performs a back flip]

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…and then change the exponent to a positive number.

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So, for example, if you’ve got 2 to the negative third power…

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…it’s the same as the reciprocal of 2… one-half… to the third power.

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½ times ½ times ½… is one-eighth.

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So, as you can see, they may not look like much, but powers are quite…powerful. [Man working out in a gym]

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They can abbreviate many big numbers…

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…and they can reduce others to rubble.

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Have fun on your power trip. Don't forget to send us a postcard. [People walking with luggage]

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