M:N:MC:5
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If 
where 
and 
which of the following equations gives 
in terms of 
Select an 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 
and then proceed to solve for 
first by squaring both sides, which gives 
and then multiplying both sides by to find 
Finally, dividing both sides by 
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 
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 is the same as the square root, and that therefore can be isolated by squaring both sides. However, the student may not understand how the negative exponent affects the base.
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.