M:N:MC:5

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If $a to the power of minus 1 half end exponent equals x comma$ where $a greater than 0$ and $x greater than 0 comma$ which of the following equations gives $a$ in terms of $x ?$

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$a equals fraction numerator 1 over denominator square root of x end fraction$

Correct Answer:

$a equals 1 over x squared$

Correct Answer:

Yes

$a equals square root of x$

Correct Answer:

$a equals minus x squared$

Correct Answer:

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Choice B is correct. There are multiple ways to approach this problem, but all require an understanding of the properties of exponents. The student may rewrite the equation as $fraction numerator 1 over denominator square root of a end fraction equals x$ and then proceed to solve for $a$ first by squaring both sides, which gives $1 over a equals x squared comma$ and then multiplying both sides by $a$ to find $1 equals a x squared.$ Finally, dividing both sides by $x squared$ isolates the desired variable.

Choice A is not the correct answer. This answer may result from a misunderstanding of the properties of exponents. The student may understand that a negative exponent can be translated to a fraction but misapply the fractional exponent.

Choice C is not the correct answer. This answer may result from a misunderstanding of the properties of exponents. A student may recognize that an exponent of $1 half$ is the same as the square root but misapply this information.

Choice D is not the correct answer. This answer may result from a misunderstanding of the properties of exponents. The student may recognize that the fractional exponent on $a$ is the same as the square root, and that therefore $a$ can be isolated by squaring both sides. However, the student may not understand how the negative exponent affects the base.

Question Difficulty:

medium

Objective:

Students must demonstrate fluency with the properties of exponents. They must be able to relate fractional exponents to radicals as well as demonstrate understanding of negative exponents.

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Question 6 of 18

M:N:MC:5

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