ShmoopTube

Where Monty Python meets your 10th grade teacher.

Search Thousands of Shmoop Videos

Fractional Exponents 3012 Views


Share It!


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.

Language:
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.

Up Next

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.

Related Videos

Numbers and Operations: Elementary Number Theory
605 Views

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
318 Views

SAT Math 7.3 Algebra and Functions

SAT Math 6.4 Algebra and Functions
486 Views

SAT Math 6.4 Algebra and Functions

Word Problems with Addition and Subtraction
4464 Views

Sometimes, we just want fewer y's...or more x's. That's why it's great to know how to add and subtract variables. In real life, though, we try to a...