Find the missing value denoted by ?
3 : 243 : : 5 : ?

Options

A. 625
B. 465
C. 3125
D. 425

Answer

To find the missing value denoted by "?", we need to analyze the relationship between the numbers given in the ratio 3 : 243 and then apply the same relationship to the number 5.

1. **Identify the relationship for the first pair (3 : 243)**:
- We can express 243 as a power of 3.
- \( 3^5 = 243 \)
- This means that 243 is equal to 3 raised to the power of 5.

2. **Establish the pattern**:
- From the first pair, we see that the first number (3) is raised to the power of 5 to get the second number (243).
- Therefore, the relationship can be written as:
\[ 3^5 = 243 \]

3. **Apply the same relationship to the second pair (5 : ?)**:
- Now we need to find out what 5 raised to the power of 5 is.
- Calculate \( 5^5 \):
\[ 5^5 = 5 \times 5 \times 5 \times 5 \times 5 \]
- First, calculate \( 5^2 = 25 \).
- Then, calculate \( 5^3 = 5 \times 25 = 125 \).
- Next, calculate \( 5^4 = 5 \times 125 = 625 \).
- Finally, calculate \( 5^5 = 5 \times 625 = 3125 \).

4. **Conclusion**:
- Therefore, the missing value denoted by "?" is \( 3125 \).

The final answer is:
\[ ? = 3125 \]