Answers: Choice A and Choice B
Step-by-step explanation:
The 4 in the denominator of the original fraction is the same as 4^1
Then use the rule that (a^b)/(a^c) = a^(b-c). That means (4^32)/(4^1) = 4^(32-1) = 4^31 pointing us to choice B as one of the answers
Then notice how (8^31)/(2^31) = (8/2)^31 = 4^31, meaning choice A is the other answer. The rule I used is (a/b)^c = (a^c)/(b^c).
Choice C is not equivalent to the original expression because 4^4*4^8 = 4^(4+8) = 4^12, which is significantly smaller than 4^31.
Choice D can be ruled out as well because 4^33 is larger than 4^31.