If 1 = 5, 2 = 25, what is 9?
Answer (1)
Observe the pattern: 1 = 5 1 and 2 = 5 2 .
Hypothesize the pattern: n = 5 n .
Apply the pattern to 9: 9 = 5 9 .
Calculate 5 9 : 5 9 = 1953125 . Therefore, the answer is 1953125 .
Explanation
Understanding the Problem We are given that 1 = 5 and 2 = 25 . We need to find the value corresponding to 9 based on the given pattern.
Identifying the Pattern Let's analyze the given information to identify a pattern. We observe that: 1 = 5 = 5 1 2 = 25 = 5 2
Applying the Pattern Based on the pattern, we can hypothesize that the value corresponding to a number n is 5 n . Therefore, for n = 9 , the corresponding value would be 5 9 .
Calculating the Value Now, we calculate 5 9 :
5 9 = 5 × 5 × 5 × 5 × 5 × 5 × 5 × 5 × 5 = 1953125
Final Answer Therefore, if 1 = 5 and 2 = 25 , then 9 = 5 9 = 1953125 .
Examples
This type of problem, where you identify a pattern and extend it, is similar to how encryption algorithms work. For example, a simple encryption might involve raising each letter's numerical value to a power and then taking the result modulo a certain number. Understanding patterns and mathematical relationships is crucial in cryptography and data security.
