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Powers and Exponents Videos 6 videos

Powers
2656 Views

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 nu...

Multiplication and Division Properties of Exponents
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Exponents desperately want to be like regular ol' numbers—so it figures they also want to be multiplied and divided.

Fractional Exponents
3012 Views

Those itty-bitty exponents are difficult to read as it is. Now they're going to be even smaller—and include fractions? Someone had better get us...

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Fractional Exponents 3012 Views


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Description:

Those itty-bitty exponents are difficult to read as it is. Now they're going to be even smaller—and include fractions? Someone had better get us our magnifying glass.

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English Language

Transcript

00:04

Fractional Exponents, a la Shmoop. When inspected under a microscope…

00:11

…fractional exponents are just like other exponents…

00:13

…except they’re smaller, they’re meaner…

00:16

… and they can spread throughout a math quiz like germs on a chew-toy.

00:21

Fractional exponents are abbreviations for taking the roots of a number.

00:25

For example, x to the power of one-sixth means the sixth root of x.

00:33

But what about those fractions that have a number other than 1 in the numerator?

00:39

What would 8 to the power of two-thirds mean?

00:43

According to the Rules of Multiplying Exponents:

00:47

Let’s say we raise x to the two-thirds power by 3.

00:54

That means we multiply x to the power of two-thirds by itself 3 times...

01:00

…adding 2/3 plus 2/3 plus 2/3 gives us 6/3. To simplify it, we divide 6 by 3 to get 2...

01:10

…which means our x is squared.

01:13

Therefore, x to the power of two-thirds is still a root.

01:18

It's the cubed root of x squared. Which makes 8 to the power of two-thirds the

01:25

cubed root of 8 squared.

01:27

Since the cube root of 8 is 2, or 2 times 2 times 2, this simplifies to two to the power

01:33

of 2

01:34

Which equals 4. So, as you can see, fractional exponents really

01:38

aren’t that scary.

01:39

Certainly less painful than a

01:55

root canal.

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