Question 495996
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:


{{{root(4,x)}}}


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 {{{root(4,x^5)}}}


x^(5/4) is the same as {{{(root(4,x))^5}}}


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 {{{root(4,x)}}}


an example:


let x = 16
x^(1/4) becomes:
16^(1/4) which becomes:
{{{root(4,16)}}} which equals 2


the rules are:


x<sup>(a/b)</sup> = {{{(root(b,x))^a}}} = {{{root(b,x^a)}}}


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