Question

Using the properties of exponents, which expression is equivalent to xx34
(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 \( x^{\frac{3}{4}} \), we can break it down using the properties of exponents.

The expression \( x^{\frac{3}{4}} \) can be interpreted as follows:

1. The denominator (4) in the exponent indicates that we are taking the fourth root.
2. The numerator (3) indicates that we are cubing the result of the fourth root.

Thus, \( x^{\frac{3}{4}} \) can be rewritten as:

\[
x^{\frac{3}{4}} = \sqrt[4]{x^3}
\]

Among the options you've provided, the equivalent expression for \( x^{\frac{3}{4}} \) is not directly listed. However, if we focus on the format of the answer:

- **4th root of x** refers to \( \sqrt[4]{x} \), which is not equivalent.
- **x** refers to \( x^1 \), which is not equivalent.
- **x4** is typically interpreted as \( x^4 \), which is also not equivalent.

None of the options provided match \( x^{\frac{3}{4}} \) directly.

If it is given clearly that the original intent was to simplify \( x^{\frac{3}{4}} \), please double-check the provided responses since none specifically align with that simplification. If you have an option indicating \( \sqrt[4]{x^3} \), that would be the correct choice.