In the questions, select the pair in which the numbers are similarly related as in the given pair.
27:9:: ?:?

Options

A. `64:8`
B. `125:5`
C. `135 : 15`
D. `729 : 81`

Explanation

To solve the analogy problem 27:9::?:?, we need to identify the relationship between the numbers in the first pair and then find a similar relationship in the options provided.

### Step-by-Step Solution:

1. **Identify the relationship in the first pair (27:9)**:
- The number 27 can be expressed as \(3^3\) (which is 3 cubed).
- The number 9 can be expressed as \(3^2\) (which is 3 squared).
- Thus, the relationship is that the first number is the cube of a number (3), and the second number is the square of the same number (3).

2. **Analyze the options given**:
- **Option 1: 64:8**
- 64 can be expressed as \(4^3\) (4 cubed).
- 8 can be expressed as \(2^3\) (2 cubed).
- This does not match the pattern (cube to square).

- **Option 2: 125:5**
- 125 can be expressed as \(5^3\) (5 cubed).
- 5 can be expressed as \(5^1\) (not a square).
- This does not match the pattern.

- **Option 3: 135:15**
- 135 is not a perfect cube.
- 15 is not a perfect square.
- This does not match the pattern.

- **Option 4: 729:81**
- 729 can be expressed as \(9^3\) (9 cubed).
- 81 can be expressed as \(9^2\) (9 squared).
- This matches the pattern where the first number is the cube of 9 and the second number is the square of 9.

3. **Conclusion**:
- The correct answer is **Option 4: 729:81** because it follows the same relationship as 27:9, where the first number is the cube of a number and the second number is the square of that same number.

### Final Answer:
729:81