Question

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

Answer 1

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

Here, we have:

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

Now, subtract the exponents:

\[
1 - \frac{3}{4} = \frac{4}{4} - \frac{3}{4} = \frac{1}{4}
\]

Therefore, we get:

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

So the expression equivalent to \( \frac{x}{x^{3/4}} \) is \( x^{1/4} \).