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Chapter 0: Problem 104

Simplify by reducing the index of the radical. $$\sqrt[4]{x^{12}}$$

Short Answer

Expert verified
\( \sqrt[4]{x^{12}} \) simplifies to \( x^3 \).

Step by step solution

01

Understand the basic property of radical

The basic property of a radical is \( \sqrt[n]{x^m} = x^{m/n} \). It means that an nth root of any number \( x^m \) can be written as a power of \( x \) where the exponent is the quotient of \( m \) divided by \( n \). Thus the given radical \( \sqrt[4]{x^{12}} \) can be written as \( x^{12/4} \).
02

Simplify the exponent

Now, divide the exponent of \( x \) by the index of the radical. In our case, divide 12 by 4 to get 3. So, \( x^{12/4} \) simplifies to \( x^3 \).
03

Final answer

The simplified form of the given radical \( \sqrt[4]{x^{12}} \) is \( x^3 \).

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