Evaluate : `6^(4)-:2^(4)`

Answer

To evaluate the expression \( \frac{6^4}{2^4} \), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the expression**: We start with the expression \( \frac{6^4}{2^4} \).

2. **Use the property of exponents**: We can apply the property of exponents which states that \( \frac{a^c}{b^c} = \left(\frac{a}{b}\right)^c \). Here, \( a = 6 \), \( b = 2 \), and \( c = 4 \).

\[ \frac{6^4}{2^4} = \left(\frac{6}{2}\right)^4 \]

3. **Simplify the fraction**: Now, simplify \( \frac{6}{2} \).

\[ \frac{6}{2} = 3 \]

4. **Rewrite the expression**: Substitute back into the expression.

\[ \left(\frac{6}{2}\right)^4 = 3^4 \]

5. **Final expression**: Therefore, we have:

\[ 6^4 \div 2^4 = 3^4 \]

6. **Calculate \( 3^4 \)**: Now, we can calculate \( 3^4 \).

\[ 3^4 = 3 \times 3 \times 3 \times 3 = 81 \]

### Final Answer:
Thus, the value of \( \frac{6^4}{2^4} \) is \( 81 \).

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