Find :
(i) `64^(1//2)`
(ii) `32^(1//5)`
(iii) `125^(1//3)`

Answer

To solve the given expressions step by step, we will evaluate each part one by one.

### Part (i): Find `64^(1/2)`

1. **Identify the base**: The base is 64.
2. **Express 64 as a power of 2**:
\[ 64 = 2^6 \]
3. **Substitute into the expression**:
\[ 64^{1/2} = (2^6)^{1/2} \]
4. **Apply the power of a power property**:
\[ (a^m)^n = a^{m \cdot n} \]
So,
\[ (2^6)^{1/2} = 2^{6 \cdot (1/2)} = 2^3 \]
5. **Calculate the final result**:
\[ 2^3 = 8 \]

### Part (ii): Find `32^(1/5)`

1. **Identify the base**: The base is 32.
2. **Express 32 as a power of 2**:
\[ 32 = 2^5 \]
3. **Substitute into the expression**:
\[ 32^{1/5} = (2^5)^{1/5} \]
4. **Apply the power of a power property**:
\[ (2^5)^{1/5} = 2^{5 \cdot (1/5)} = 2^1 \]
5. **Calculate the final result**:
\[ 2^1 = 2 \]

### Part (iii): Find `125^(1/3)`

1. **Identify the base**: The base is 125.
2. **Express 125 as a power of 5**:
\[ 125 = 5^3 \]
3. **Substitute into the expression**:
\[ 125^{1/3} = (5^3)^{1/3} \]
4. **Apply the power of a power property**:
\[ (5^3)^{1/3} = 5^{3 \cdot (1/3)} = 5^1 \]
5. **Calculate the final result**:
\[ 5^1 = 5 \]

### Final Answers:
(i) `64^(1/2) = 8`
(ii) `32^(1/5) = 2`
(iii) `125^(1/3) = 5`