Final answer:
The question is about finding the missing term in a mathematical analogy. The relationship between the first pair of numbers is determined by raising the first number to the 4th power. Applying this relationship to the second pair gives us 5 to the power of 4, which equals 625.
Step-by-step explanation:
In this question, we are dealing with an analogy represented by two ratios or proportions, and we need to find the missing term. The analogy is 4:256 :: 5:?. To solve this, we must find the relationship between the numbers in the first ratio and then apply that to the second ratio. The first ratio, 4:256, can be seen as exponentiation where 4 to the power of 4 equals 256. Therefore, we need to raise 5 to the 4th power for the second ratio to maintain the analogy. 5 to the power of 4 equals 625. So, the analogy would be 4:256::5:625.
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