Using the properties of exponents, which expression is equivalent to xx34

Question

?(1 point)
Responses

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

x4
x superscript 4 baseline

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

x
x

Answer 1

To determine which expression is equivalent to \( x^{\frac{3}{4}} \), we can analyze each option.

1. \( \frac{1}{\sqrt[4]{x}} \): This can be rewritten using the properties of exponents:

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

   This is not equivalent to \( x^{\frac{3}{4}} \).

2. \( x^4 \): This is clearly not equivalent to \( x^{\frac{3}{4}} \).

3. \( \sqrt[4]{x} \): This can be rewritten as:

   \[ \sqrt[4]{x} = x^{\frac{1}{4}} \]

   This is also not equivalent to \( x^{\frac{3}{4}} \).

4. \( x \): This can be written as \( x^1 \), which is not equivalent to \( x^{\frac{3}{4}} \).

None of the provided options are equivalent to \( x^{\frac{3}{4}} \). Thus, it seems there is no correct answer in the choices provided for the expression \( x^{\frac{3}{4}} \). If you meant to provide an additional option or a different expression, please share that!