Question

Using the properties of exponents, which expression is equivalent to x/x3/4
(1 point)
Responses

x−−√4
4th root of x

1x√4
the fraction with numerator 1 and denominator 4th root of x

x
x

x4

Answer 1

To simplify the expression \( \frac{x}{x^{3/4}} \) using the properties of exponents, we can apply the rule that states \( \frac{a^m}{a^n} = a^{m-n} \).

Here, we have:

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

Now, \( x^{\frac{1}{4}} \) can also be expressed as the 4th root of \( x \), which is written as:

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

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

**4th root of x**.