Amy P.

asked • 03/17/14# What is a fractional exponent? How are fractional exponents and radicals related? Do you prefer using fractional exponents or radicals when performing operation

## 4 Answers By Expert Tutors

Parviz F. answered • 03/18/14

Mathematics professor at Community Colleges

^{n}√ X

^{n}= X

^{n})

^{1/n}

^{n(1/n) }= X

^{n}√ .

Kay G. answered • 03/17/14

~20 Years Accounting Tutoring Experience

a

^{x}is where x is the exponent

So 2

^{3}has an exponent of 3.

A fractional exponent is the same thing, except the x is going to be a fraction like:

2

^{(1/3)}

Which is 2 to the 1/3rd. The (1/3) is the exponent and it's a fraction; hence, fractional exponent.

A radical is with the √ sign. So square root, cubed root, etc are radicals. Like:

^{x}√a means the x root of a.

^{2}√16 means the square root of 16 (which is 4). (Usually just written as √16 with the 2 being understood. That only works when it's just a 2.)

A fractional exponent can be written as a radical. As already shown:

^{x}√(a

^{y}) means x root of (a

^{y})

2

^{(1/3)}(fractional exponent) can be written as

^{3}√2 (radical)

4

^{(2/3)}(fractional exponent) can be written as

^{3}√(4

^{2}) (radical)

Note where the numerator and denominator of the fraction in the exponent are when you do it as a radical. (numerator inside and denominator outside) When the numerator is 1, you don't write it. In my example 2

^{(1/3)}=

^{3}√2 note I never put the 1 exponent on the radical. 2

^{1}= 2 so the 1 is not needed and we leave it off.

You have to decide which is easier to solve. :-) If you're doing it manually, you just about have to turn it into a radical. (2 multiplied times itself 1/3 times? Sounds a little weird, huh?) If you're using a calculator either can be just as easy depending on the calculator. But I suspect since you're just learning these, you're doing them manually.

Steve S.

03/18/14

Kay G.

03/18/14

Ebenezer O. answered • 03/17/14

Aerospace Engr & Air Traffic Control Grad For General Ed. Tutoring

^{½}is the same as √x

^{¼}is the same as

^{4}√x

^{¾}is the same as

^{4}√(x)

^{3}

^{a/b}is the same as

^{b}√(x)

^{a}

Jason S. answered • 03/17/14

Science/math--college level and below

^{(1/2) }. If you plug that into a calculator you should get 2 either way. Another example is the cube root of 8 can also be expressed at 8

^{(1/3)}. There is a recognizable pattern:

**n**root of any number (

^{th}**x**) can also be expressed as:

**x**

^{(1/n) }.## Still looking for help? Get the right answer, fast.

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Jimin B.

04/28/18