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Question 6 of 18

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M:N:MC:5

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SAT

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Passport to Advanced Math

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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 ?

Select an Answer

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

Correct Answer: 
No

a equals 1 over x squared

Correct Answer: 
Yes

a equals square root of x

Correct Answer: 
No

a equals minus x squared

Correct Answer: 
No

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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.