Evaluate each of the following :
`(i)16^(1//2)" "(ii)243^(1//5)" "(iii)81^(1//4)`

Explanation

To evaluate the expressions given, we will follow the steps outlined in the video transcript. Let's solve each part step by step.

### (i) Evaluate \( 16^{\frac{1}{2}} \)

1. **Rewrite 16 as a power of 4**:
\[ 16 = 4^2 \]

2. **Substitute into the expression**:
\[ 16^{\frac{1}{2}} = (4^2)^{\frac{1}{2}} \]

3. **Apply the power of a power rule**:
\[ (a^m)^n = a^{m \cdot n} \implies (4^2)^{\frac{1}{2}} = 4^{2 \cdot \frac{1}{2}} = 4^1 \]

4. **Simplify**:
\[ 4^1 = 4 \]

### Answer for (i):
\[ 16^{\frac{1}{2}} = 4 \]

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### (ii) Evaluate \( 243^{\frac{1}{5}} \)

1. **Rewrite 243 as a power of 3**:
\[ 243 = 3^5 \]

2. **Substitute into the expression**:
\[ 243^{\frac{1}{5}} = (3^5)^{\frac{1}{5}} \]

3. **Apply the power of a power rule**:
\[ (3^5)^{\frac{1}{5}} = 3^{5 \cdot \frac{1}{5}} = 3^1 \]

4. **Simplify**:
\[ 3^1 = 3 \]

### Answer for (ii):
\[ 243^{\frac{1}{5}} = 3 \]

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### (iii) Evaluate \( 81^{\frac{1}{4}} \)

1. **Rewrite 81 as a power of 3**:
\[ 81 = 3^4 \]

2. **Substitute into the expression**:
\[ 81^{\frac{1}{4}} = (3^4)^{\frac{1}{4}} \]

3. **Apply the power of a power rule**:
\[ (3^4)^{\frac{1}{4}} = 3^{4 \cdot \frac{1}{4}} = 3^1 \]

4. **Simplify**:
\[ 3^1 = 3 \]

### Answer for (iii):
\[ 81^{\frac{1}{4}} = 3 \]

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### Final Answers:
1. \( 16^{\frac{1}{2}} = 4 \)
2. \( 243^{\frac{1}{5}} = 3 \)
3. \( 81^{\frac{1}{4}} = 3 \)

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