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Basic Operations Videos 58 videos

Operations with Rational Expressions
8687 Views

It's impressive that these expressions are able to stay so rational even when they're having operations performed on them.

Numbers and Operations: Elementary Number Theory
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Jack and Jill went up the hill to fetch a pail of water. But what happened when they got up there? They’ve been gone an awfully long time…

SAT Math 7.3 Algebra and Functions
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SAT Math 7.3 Algebra and Functions

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Powers 2656 Views


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Description:

Numbers have friends in high places: they're called powers. And yes, they are powerful. They can make a single digit number turn into a 10 digit number. Its not magic—it's math.

Language:
English Language

Transcript

00:00

Powers, a la Shmoop. Sometimes, the greatest power comes in the

00:11

smallest packages. Take David, for example. Goliath never even

00:17

knew what hit him. How about Napoleon? He certainly didn’t

00:22

win any battles because of his height. And then there’s Stewie Griffin. He’s

00:28

barely a foot tall and yet he has already mastered time travel.

00:32

There’s a reason we have something in math called a “power.”

00:35

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

00:43

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

00:47

in order to make them more manageable. But while they may not look that important,

00:53

don’t be fooled. An exponent can take an expression like 5

00:58

times 5 times 5 times 5, and express it this way:

01:01

We are multiplying four 5’s together, so our exponent is the number 4.

01:06

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

01:12

As you can imagine, you might have many more numbers to multiply together than just four

01:16

of them.

01:17

Do you really want to write out numbers the long way?

01:21

We didn’t think so.

01:25

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

01:28

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

01:32

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

01:39

is always equal to one. An exponent can also be negative.

01:45

In that case, you will need to take the reciprocal of the number…

01:49

…and then change the exponent to a positive number.

01:53

So, as you can see, they may not look like much, but they are “powerful.”

02:02

They can abbreviate many big numbers…

02:04

…and they can reduce others to rubble. Have fun on your power trip. Send us a postcard.

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