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Advanced Math / Equivalent expressions Difficulty: Medium

If $x is not equal to 0$ , which of the following expressions is equivalent to $the fraction with numerator the square root of 16 x to the fourth power, y to the eighth power, end root, and denominator x cubed, end fraction$ ?

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Explanation

Choice D is correct. Taking the square root of an exponential expression halves the exponent, so $the fraction with numerator the square root of, 16 x to the fourth power times y to the eighth power, end root, and denominator x cubed, end fraction, equals, the fraction with numerator 4 x squared, times y to the fourth power, and denominator x cubed$ , which further reduces to $the fraction with numerator 4, y to the fourth power, and denominator x$ . This can be rewritten as $4, x to the negative 1 power, times y to the fourth power$ .

Choice A is incorrect and may result from neglecting the denominator of the given expression and from incorrectly calculating the square root of 16. Choice B is incorrect and may result from rewriting $1 over x$ as $x to the first power$ rather than $x to the negative 1 power$ . Choice C is incorrect and may result from taking the square root of the variables in the numerator twice instead of once.