Question

Using the properties of exponents, which expression is equivalent to x/x^3/4

x
(1)/(\root(4)(x))
\root(4)(x)
x

Answer 1

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

Recall that \( \frac{a^m}{a^n} = a^{m-n} \).

So in this case:

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

Now, we can represent \( x^{1/4} \) as \( \sqrt[4]{x} \).

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

\(\sqrt[4]{x}\) or \(\root{4}{x}\).

Therefore, the correct answer is:

\(\root{4}{x}\)