Find sub-triplicate ratio of :
(i) `64 : 27`
(ii) `x^(3) : 125y^(3)`

Answer

To find the sub-triplicate ratio of the given ratios, we need to take the cube root of each term in the ratio. Let's solve the question step by step.

### Step-by-Step Solution

#### Part (i): Find the sub-triplicate ratio of `64 : 27`

1. **Identify the terms**: The terms in the ratio are 64 and 27.

2. **Find the cube roots**:
- The cube root of 64 is calculated as follows:
\[ \sqrt[3]{64} = \sqrt[3]{4^3} = 4 \]
- The cube root of 27 is calculated as follows:
\[ \sqrt[3]{27} = \sqrt[3]{3^3} = 3 \]

3. **Write the sub-triplicate ratio**:
\[ \text{Sub-triplicate ratio} = 4 : 3 \]

#### Part (ii): Find the sub-triplicate ratio of `x^3 : 125y^3`

1. **Identify the terms**: The terms in the ratio are \(x^3\) and \(125y^3\).

2. **Find the cube roots**:
- The cube root of \(x^3\) is:
\[ \sqrt[3]{x^3} = x \]
- The cube root of \(125y^3\) is calculated as follows:
\[ \sqrt[3]{125y^3} = \sqrt[3]{125} \cdot \sqrt[3]{y^3} = 5y \]
(since \(125 = 5^3\))

3. **Write the sub-triplicate ratio**:
\[ \text{Sub-triplicate ratio} = x : 5y \]

### Final Answers
- (i) The sub-triplicate ratio of `64 : 27` is `4 : 3`.
- (ii) The sub-triplicate ratio of `x^3 : 125y^3` is `x : 5y`.