Which of the following is equal tofor all integers x and y?

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问题 Which of the following is equal to

for all integers x and y?

选项 A、4^-x
B、4^-y
C、2^xy
D、4^x
E、4^y

答案B

解析 Simplifying the fraction

. The only answer choice with 2 as the base is Choice C, 2^xy, which is clearly not the correct answer. Since all the other answer choices have 4 as the base, it is a good idea to rewrite 2^-2y as an expression with 4 as the base, as follows.

Thus the correct answer is Choice B.
This explanation uses the following strategies.
Strategy 5: Simplify an Arithmetic or Algebraic Representation
Strategy 8: Search for a Mathematical Relationship

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Which of the following is equal tofor all integers x and y?

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