Find the values of :-
(1)`(8)^(1//3)`
(2)`(64)^(1//2)`
(3)`4^(5//2)`
(4)`(36)^(3//2)`
(5)`(27)^(2//3)`

Answer

Let's solve the given problems step by step.

### Problem 1: Find `(8)^(1/3)`

1. **Identify the expression**: We need to find the cube root of 8.
2. **Express 8 as a power of a prime**: \( 8 = 2^3 \).
3. **Apply the exponent rule**:
\[ (8)^{1/3} = (2^3)^{1/3} = 2^{3 \cdot (1/3)} = 2^1 = 2. \]
4. **Final answer**: \( (8)^{1/3} = 2 \).

### Problem 2: Find `(64)^(1/2)`

1. **Identify the expression**: We need to find the square root of 64.
2. **Express 64 as a power of a prime**: \( 64 = 8^2 = (2^3)^2 = 2^6 \).
3. **Apply the exponent rule**:
\[ (64)^{1/2} = (2^6)^{1/2} = 2^{6 \cdot (1/2)} = 2^3 = 8. \]
4. **Final answer**: \( (64)^{1/2} = 8 \).

### Problem 3: Find `4^(5/2)`

1. **Identify the expression**: We need to calculate \( 4^{5/2} \).
2. **Express 4 as a power of a prime**: \( 4 = 2^2 \).
3. **Apply the exponent rule**:
\[ 4^{5/2} = (2^2)^{5/2} = 2^{2 \cdot (5/2)} = 2^5. \]
4. **Calculate \( 2^5 \)**:
\[ 2^5 = 32. \]
5. **Final answer**: \( 4^{5/2} = 32 \).

### Problem 4: Find `(36)^(3/2)`

1. **Identify the expression**: We need to calculate \( 36^{3/2} \).
2. **Express 36 as a power of a prime**: \( 36 = 6^2 \).
3. **Apply the exponent rule**:
\[ (36)^{3/2} = (6^2)^{3/2} = 6^{2 \cdot (3/2)} = 6^3. \]
4. **Calculate \( 6^3 \)**:
\[ 6^3 = 216. \]
5. **Final answer**: \( (36)^{3/2} = 216 \).

### Problem 5: Find `(27)^(2/3)`

1. **Identify the expression**: We need to calculate \( 27^{2/3} \).
2. **Express 27 as a power of a prime**: \( 27 = 3^3 \).
3. **Apply the exponent rule**:
\[ (27)^{2/3} = (3^3)^{2/3} = 3^{3 \cdot (2/3)} = 3^2. \]
4. **Calculate \( 3^2 \)**:
\[ 3^2 = 9. \]
5. **Final answer**: \( (27)^{2/3} = 9 \).

### Summary of Answers:
1. \( (8)^{1/3} = 2 \)
2. \( (64)^{1/2} = 8 \)
3. \( 4^{5/2} = 32 \)
4. \( (36)^{3/2} = 216 \)
5. \( (27)^{2/3} = 9 \)