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To solve the equation:

\[
\frac{1}{x^2} - 4x^{\frac{1}{4}} = 0
\]

let's follow these steps:

1. **Isolate terms:** Move one term to the other side to make it easier to solve for \( x \).

   \[
   \frac{1}{x^2} = 4x^{\frac{1}{4}}
   \]

2. **Rewrite in terms of powers:** Rewrite both terms in terms of powers of \( x \).

   - The left side, \( \frac{1}{x^2} \), is equivalent to \( x^{-2} \).
   - The right side, \( 4x^{\frac{1}{4}} \), is already in terms of a power of \( x \).

   So the equation becomes:

   \[
   x^{-2} = 4x^{\frac{1}{4}}
   \]

3. **Rewrite equation by making the powers equal:** Divide both sides by \( x^{\frac{1}{4}} \) to express it as a single power of \( x \).

   This yields:

   \[
   x^{-\frac{9}{4}} = 4
   \]

4. **Solve for \( x \):** Rewrite \( x^{-\frac{9}{4}} = 4 \) in terms of radicals and solve for \( x \) by taking appropriate powers.

Learn how to solve the rational exponential equation 1/x^2 - 4x^(1/4) = 0. This solution covers key algebraic concepts, properties of exponents, and rational equation techniques, ideal for students in Grades 11-12.

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