Question

Using the properties of exponents, which expression is equivalent to x/x 3/4 ?(1 point)
Responses

x−−√4
root index 4 Start Root x End Root

x
x

x4
x superscript 4 baseline

1​x√4

Answer 1

To simplify the expression \( \frac{x}{x^{3/4}} \), we can use the properties of exponents.

We know that when dividing two expressions with the same base, we subtract the exponents:

\[
\frac{x^a}{x^b} = x^{a-b}
\]

In this case, we can rewrite \( x \) as \( x^1 \):

\[
\frac{x^1}{x^{3/4}} = x^{1 - \frac{3}{4}} = x^{\frac{4}{4} - \frac{3}{4}} = x^{\frac{1}{4}}
\]

Thus, \( \frac{x}{x^{3/4}} \) simplifies to \( x^{1/4} \), which is the same as \( \sqrt[4]{x} \) (the fourth root of \( x \)).

So the expression equivalent to \( \frac{x}{x^{3/4}} \) is:

\[
\sqrt[4]{x}
\]

The correct response is:

**root index 4 Start Root x End Root** (which represents \( \sqrt[4]{x} \)).