QuestionSimplify the radical. Assume that the variable represents a positive real number. $\sqrt[4]{\frac{x^{12}}{16}}$
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. $\sqrt[4]{\frac{x^{12}}{16}}=$ $\square$ (Simplify your answer. Use integers or fractions for any numbers in the expression.) B. The radical does not represent a real number.

Studdy Solution
Simplify the fourth root of the numerator:
$\sqrt[4]{x^{12}} = x^{\frac{12}{4}} = x^3$
Simplify the fourth root of the denominator:
$\sqrt[4]{16} = \sqrt[4]{2^4} = 2$
Combine the simplified parts:
$\frac{x^3}{2}$
The simplified expression is:
$\boxed{\frac{x^3}{2}}$

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