Question

Using the properties of exponents, which expression is equivalent to xx34?(1 point)
Responses

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

x
x

1​x√4
Start Fraction 1 over root index 4 Start Root x End Root End Fraction

x4

Answer 1

To determine which expression is equivalent to \( x^{x34} \), we first need to simplify what \( x^{x34} \) means. Here, it seems there's a misunderstanding in notation. I will interpret "xx34" as simply \( x^{(3/4)} \), given there is a mention of a fraction in one of the choices.

Now, let's analyze the options given:

1. \( \sqrt[4]{x} \)
This is equivalent to \( x^{1/4} \).

2. \( x \)
This is simply \( x^{1} \).

3. \( \frac{1}{\sqrt[4]{x}} \)
This is equivalent to \( x^{-1/4} \).

4. \( x^4 \)
This is simply \( x^{4} \).

Given the assumption that \( x^{x34} \) is meant to represent \( x^{3/4} \), let's find the equivalent expression.

- \( \sqrt[4]{x} \) ➔ not equivalent
- \( x \) ➔ not equivalent
- \( \frac{1}{\sqrt[4]{x}} \) ➔ not equivalent
- \( x^4 \) ➔ not equivalent

If we still assume it is \( x^{3/4} \), none of the options would be equal to \( x^{3/4} \). However, if there was a typo or misrepresentation, and it means something different, clarification is needed.

But based on what you've provided, none of the given responses are equivalent to \( x^{(3/4)} \). Please confirm or clarify the expression you intended.