Simplify `6^(6)-:3^(3)` and write in exponential form.

Answer

To simplify the expression \( 6^6 \div 3^3 \) and write it in exponential form, we can follow these steps:

### Step 1: Rewrite the base 6 in terms of its prime factors
The number 6 can be expressed as the product of its prime factors:
\[ 6 = 2 \times 3 \]
Thus, we can rewrite \( 6^6 \) as:
\[ 6^6 = (2 \times 3)^6 \]

### Step 2: Apply the exponent rule
Using the property of exponents that states \( (a \times b)^n = a^n \times b^n \), we can expand \( (2 \times 3)^6 \):
\[ (2 \times 3)^6 = 2^6 \times 3^6 \]

### Step 3: Substitute back into the original expression
Now we substitute back into the original expression:
\[ 6^6 \div 3^3 = \frac{2^6 \times 3^6}{3^3} \]

### Step 4: Simplify the division of the powers of 3
Using the exponent rule that states \( \frac{a^m}{a^n} = a^{m-n} \), we can simplify \( \frac{3^6}{3^3} \):
\[ \frac{3^6}{3^3} = 3^{6-3} = 3^3 \]

### Step 5: Combine the results
Now, we can combine the results:
\[ \frac{2^6 \times 3^6}{3^3} = 2^6 \times 3^3 \]

### Final Result
Thus, the simplified form of \( 6^6 \div 3^3 \) in exponential form is:
\[ 2^6 \times 3^3 \]

---