Questions: Simplify the radical expression, where n is an odd positive integer. sqrt[n]x^(4n) Write your answer in the form A, sqrt[n]B, or A sqrt[n]B, where A and B are constants or expressions in x. Use at most one radical in your answer, and at most one absolute value symbol in your expression for A.

Simplify the radical expression, where n is an odd positive integer.

sqrt[n]x^(4n)

Write your answer in the form A, sqrt[n]B, or A sqrt[n]B, where A and B are constants or expressions in x. Use at most one radical in your answer, and at most one absolute value symbol in your expression for A.
Transcript text: Simplify the radical expression, where $n$ is an odd positive integer. \[ \sqrt[n]{x^{4 n}} \] Write your answer in the form $A, \sqrt[n]{B}$, or $A \sqrt[n]{B}$, where $A$ and $B$ are constants or expressions in x . Use at most one radical in your answer, and at most one absolute value symbol in your expression for $A$.
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Solution

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Simplify the radical expression \( \sqrt[n]{x^{4n}} \) where \( n \) is an odd positive integer.

Identify the expression to simplify.

The expression given is \( \sqrt[n]{x^{4n}} \).

Apply the property of exponents to simplify.

Using the property \( \sqrt[n]{a^m} = a^{m/n} \), we rewrite the expression as \( (x^{4n})^{1/n} \).

Simplify the exponent.

This results in \( x^{4n/n} = x^4 \).

The simplified expression is \( \boxed{x^4} \).

The final answer is \( \boxed{x^4} \).

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