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To rationalize the numerator \(\frac{\sqrt[5]{x^4 z}}{y}\), we aim to eliminate the fifth root from the numerator. 

The expression in the numerator is \(\sqrt[5]{x^4 z}\), which is the fifth root of \(x^4 z\). To rationalize it, we multiply both the numerator and denominator by an appropriate term so that the root becomes a whole power.

Here’s the step-by-step process:

### Step 1: Identify the needed factor
We currently have \(\sqrt[5]{x^4 z}\) in the numerator. To eliminate the fifth root, we need to multiply by a term that will make the power of \(x^4\) and \(z\) inside the radical a multiple of 5. 

- For \(x^4\), we need to multiply by \(\sqrt[5]{x}\) to make the exponent 5.
- For \(z\), we need to multiply by \(\sqrt[5]{z^4}\) to make the exponent 5.

Thus, we multiply both the numerator and denominator by \(\sqrt[5]{x z^4}\).

### Step 2: Multiply the numerator and denominator
Multiply both the numerator and denominator by \(\sqrt[5]{x z^4}\):

\[
\frac{\sqrt[5]{x^4 z}}{y} \times \frac{\sqrt[5]{x z^4}}{\sqrt[5]{x z^4}} = \frac{\sqrt[5]{x^4 z} \times \sqrt[5]{x z^4}}{y \times \sqrt[5]{x z^4}}
\]

### Step 3: Simplify the numerator
Using the property of radicals \(\sqrt[n]{a} \times \sqrt[n]{b} = \sqrt[n]{a \cdot b}\), we get:

\[
\sqrt[5]{(x^4 z) \cdot (x z^4)} = \sqrt[5]{x^5 z^5} = x z
\]

So the numerator becomes \(xz\), and the denominator is \(y \cdot \sqrt[5]{x z^4}\).

### Final Result:
The rationalized expression is:

\[
\frac{xz}{y \cdot \sqrt[5]{x z^4}}
\]

Would you like more details or have any other questions?

### Here are 5 related questions:
1. How do you rationalize a denominator containing radicals?
2. What is the general approach for rationalizing cube roots?
3. How does rationalizing higher-order roots differ from square roots?
4. Can you rationalize an expression involving multiple variables inside a radical?
5. How do fractional exponents relate to radicals?

### Tip:
Always check if the indices of radicals or exponents can be combined or simplified before multiplying for rationalization!

Rationalize the numerator: \(\frac{\sqrt[5]{x^4 z}}{y}\).

Learn how to rationalize the numerator \(\frac{\sqrt[5]{x^4 z}}{y}\) using the properties of radicals and exponents. This step-by-step guide will walk you through the process of eliminating the fifth root in the numerator by multiplying the appropriate terms. Ideal for students in Grades 10-12.

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