SOLUTION: I am confused by this question, particularly because of the variable being used instead of a real number. Rewrite without exponents: x^1/4 (fraction, not division) Thanks.

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Question 495996: I am confused by this question, particularly because of the variable being used instead of a real number.
Rewrite without exponents:
x^1/4 (fraction, not division)
Thanks.
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
x^(1/4) is the expression.

you are taking x and raising it to the power of (1/4)

raising something to the power of (1/n) means taking the nth root of that something.

in this expression, you are taking the 4th root of x.

that would be shown as:

in general, the expression of:

x^(a/b) raises x to the power of a and then takes the bth root of the result.
alternatively, x^(a/b) takes the bth root of x and then raises it to the power of a.

an example will help clarify this:

x^(5/4) is the same as (x^5)^(1/4) which is the same as

x^(5/4) is the same as

an example will help clarify this.

let x = 16
x^5 = 16^5 = 1048576
1048576^(1/4) = 32

same example, only working the other way (taking the root first and then taking the power).

let x = 16
x^(1/4) = 2
2^5 = 32

whether you take the root first or you raise to the power first doesn't matter.
you get the same answer each time.

your problem is:

x^(1/4)
they want you to rewrite without exponents.
x^(1/4) is equivalent to

an example:

let x = 16
x^(1/4) becomes:
16^(1/4) which becomes:
which equals 2

the rules are:

x^(a/b) = =

in your problem, a was equal to 1.
is just shown as x.