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Powers and Exponents Videos 6 videos
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...
Exponents desperately want to be like regular ol' numbers—so it figures they also want to be multiplied and divided.
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...
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.
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.
Full Transcript
- 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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