Express in the form of x^n?

Question

5th root of x divided by x

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Answer 1 · 2018-01-27T16:09:44

#x^(-4/5)#

Not exactly sure if this is what you are looking for.

#root(5)(x)=x^(1/5)#

#x^(1/5)/x=x^(1/5-1)= x^(-4/5)#

Answer 2 · 2018-01-27T16:13:19

See a solution process below:

We can write this expression as:

#root(5)(x)/x#

First, use this rule for exponents to rewrite the numerator:

#root(color(red)(n))(x) = x^(1/color(red)(n))#

#root(color(red)(5))(x)/x => x^(1/color(red)(5))/x#

Next, use this rule of exponents to rewrite the denominator:

#a = a^color(red)(1)#

#x^(1/5)/x => x^(1/5)/x^color(red)(1)#

Now, use this rule of exponents to simplify the expression:

#x^color(red)(a)/x^color(blue)(b) = 1/x^(color(blue)(b)-color(red)(a))#

#x^(color(red)(1/5))/x^color(blue)(1) => 1/x^(color(blue)(1)-color(red)(1/5)) => 1/x^(4/5)#

We can also rewrite this as a negative exponent using this rule:

#1/x^color(red)(a) = x^color(red)(-a)#

#1/x^(4/5) => x^(-4/5)#