Properties of Rational Exponents Quick Check

Question

2 of 52 of 5 Items
Question
Using the properties of exponents, which expression is equivalent to xx34
?(1 point)
Responses

x
x

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

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

x4
x superscript 4 baseline
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Answer 1

To simplify the expression \( x^{x \frac{3}{4}} \), we can break it down:

1. The expression can be rewritten using properties of exponents:

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

This does not directly match the options provided, which appear to relate to extracting roots or manipulating the exponent in a different way.

Next, we need to clarify or examine the options:

1. \( x^{\frac{1}{\sqrt[4]{x}}} \): This can be simplified further but does not appear relevant here.

2. \( \frac{1}{\sqrt[4]{x}} \): This represents \( x^{-\frac{1}{4}} \).

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

4. \( x^4 \): This indicates \( x \) raised to the power of \( 4 \).

Since none of these exactly match the required expression, let's analyze if they can be represented in rational exponents.

It appears that the expression \( x^{x \frac{3}{4}} \) is not in the list of options you provided, and it's essential to confirm if the intention was to ask for a different starting point or if information about the input may have been omitted. If referring to just one of these options based on properties, none fit perfectly.

If you need such a simplification, consider clarifying the task or confirming the intended equivalence.