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Simplify the radical expression. 14x14 \sqrt{14x^{14}} Write your answer in the form A A , B \sqrt{B} , or AB A\sqrt{B} , where A A and B B are constants or expressions in x x . Use at most one radical in your answer, and at most one absolute value symbol in your expression for A A . ______

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Q. Simplify the radical expression. 14x14 \sqrt{14x^{14}} Write your answer in the form A A , B \sqrt{B} , or AB A\sqrt{B} , where A A and B B are constants or expressions in x x . Use at most one radical in your answer, and at most one absolute value symbol in your expression for A A . ______
  1. Identify and Multiply: Identify the expression and use the multiplication property of square roots.\newline14x14=14×x14\sqrt{14x^{14}} = \sqrt{14} \times \sqrt{x^{14}}
  2. Express as Square Term: Recognize that x14x^{14} can be expressed as a square term.\newlinex14=(x7)2x^{14} = (x^7)^2
  3. Simplify Square Root: Simplify the square root of the square term.\newline(x7)2=(x7)22=x7\sqrt{(x^7)^2} = (x^7)^{\frac{2}{2}} = x^7\newlineHowever, since we are taking the square root of a variable to an even power, we must consider the absolute value to ensure the result is non-negative.\newline(x7)2=x7\sqrt{(x^7)^2} = |x^7|
  4. Consider Absolute Value: Combine the simplified terms to get the final expression.\newline14x14=14x7\sqrt{14x^{14}} = \sqrt{14} \cdot |x^7|\newlineSo, the simplified radical expression is x714|x^7| \sqrt{14}.

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