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Advanced Math / Equivalent expressions Difficulty: Medium

Which of the following is equivalent to $the fourth root of, x squared, plus 8 x, plus 16, end root$ , where $x is greater than 0$ ?

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Explanation

Choice D is correct. The given expression can also be written as $open parenthesis, x squared, plus 8, x, plus 16, close parenthesis, raised to the one fourth power$ . The trinomial $x squared, plus 8, x, plus 16$ can be rewritten in factored form as $open parenthesis, x plus 4, close parenthesis, squared$ . Thus, the entire expression can be rewritten as $open parenthesis, open parenthesis, x plus 4, close parenthesis, squared, close parenthesis, raised to the one fourth power$ . Simplifying the exponents yields $open parenthesis, x plus 4, close parenthesis, raised to the one half power$ .

Choices A, B, and C are incorrect and may result from errors made when simplifying the exponents in the expression $open parenthesis, open parenthesis, x plus 4, close parenthesis, squared, close parenthesis, raised to the one fourth power$ .