Simplify
(i) `3^((1)/(4)) xx 5^((1)/(4))` (ii) `2^((5)/(8)) xx 3^((5)/(8))` (iii) ` 6^((1)/(2)) xx 7^((1)/(2))`

Answer

To simplify the given expressions, we will use the property of exponents which states that when multiplying two numbers with the same exponent, we can combine them under a single exponent.

### Step-by-Step Solution:

**(i)** Simplify \(3^{\frac{1}{4}} \times 5^{\frac{1}{4}}\)

1. **Identify the common exponent**: Both terms have the exponent \(\frac{1}{4}\).
2. **Combine the bases**: Multiply the bases \(3\) and \(5\).
\[ 3 \times 5 = 15 \]
3. **Apply the common exponent**: Write the result with the common exponent.
\[ 15^{\frac{1}{4}} \]

**Final result for (i)**:
\[ 15^{\frac{1}{4}} \]

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**(ii)** Simplify \(2^{\frac{5}{8}} \times 3^{\frac{5}{8}}\)

1. **Identify the common exponent**: Both terms have the exponent \(\frac{5}{8}\).
2. **Combine the bases**: Multiply the bases \(2\) and \(3\).
\[ 2 \times 3 = 6 \]
3. **Apply the common exponent**: Write the result with the common exponent.
\[ 6^{\frac{5}{8}} \]

**Final result for (ii)**:
\[ 6^{\frac{5}{8}} \]

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**(iii)** Simplify \(6^{\frac{1}{2}} \times 7^{\frac{1}{2}}\)

1. **Identify the common exponent**: Both terms have the exponent \(\frac{1}{2}\).
2. **Combine the bases**: Multiply the bases \(6\) and \(7\).
\[ 6 \times 7 = 42 \]
3. **Apply the common exponent**: Write the result with the common exponent.
\[ 42^{\frac{1}{2}} \]

**Final result for (iii)**:
\[ 42^{\frac{1}{2}} \]

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### Summary of Results:
- (i) \(15^{\frac{1}{4}}\)
- (ii) \(6^{\frac{5}{8}}\)
- (iii) \(42^{\frac{1}{2}}\)