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Radical form into exponential form and exponential form into radical form.

The given expression is:

\[
\sqrt[4]{(3xyz)^3}
\]

### Converting to Exponential Form:
The general form of a radical can be written as an exponent:
\[
\sqrt[n]{a^m} = a^{m/n}
\]
Applying this to your expression:

\[
\sqrt[4]{(3xyz)^3} = (3xyz)^{3/4}
\]

### Converting from Exponential to Radical Form:
If you start with \( (3xyz)^{3/4} \), you convert it back to radical form:

\[
(3xyz)^{3/4} = \sqrt[4]{(3xyz)^3}
\]

Would you like more details?

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**Relative Questions:**
1. How do you simplify expressions with fractional exponents?
2. What are the properties of exponents used in these conversions?
3. How do you handle radicals involving variables?
4. How does exponentiation affect product operations like \( xyz \)?
5. What are common errors to avoid when working with radicals?

**Tip:** When converting between forms, always apply exponent rules carefully to each factor.

Convert the radical expression \( \sqrt[4]{(3xyz)^3} \) into exponential form and vice versa.

Learn how to convert the radical expression \( \sqrt[4]{(3xyz)^3} \) into exponential form, \( (3xyz)^{3/4} \), and vice versa. This problem covers key algebraic concepts and exponentiation rules. Suitable for students in Grades 9-11.

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