Simplify and write the in the exponential form:
`(2^(4)xx2xx7^(3)xx7^(6))/(2^(3)xx7^(4))`

Answer

To simplify the expression \((2^{4} \times 2 \times 7^{3} \times 7^{6}) / (2^{3} \times 7^{4})\) and write it in exponential form, we can follow these steps:

### Step 1: Combine the terms in the numerator
The numerator is \(2^{4} \times 2 \times 7^{3} \times 7^{6}\). We can combine the powers of 2 and the powers of 7.

For the base 2:
\[ 2^{4} \times 2 = 2^{4} \times 2^{1} = 2^{4 + 1} = 2^{5} \]

For the base 7:
\[ 7^{3} \times 7^{6} = 7^{3 + 6} = 7^{9} \]

So, the numerator simplifies to:
\[ 2^{5} \times 7^{9} \]

### Step 2: Write the expression with the simplified numerator
Now we can rewrite the entire expression:
\[ \frac{2^{5} \times 7^{9}}{2^{3} \times 7^{4}} \]

### Step 3: Apply the law of exponents for division
Using the law of exponents \(\frac{a^{m}}{a^{n}} = a^{m-n}\), we can simplify the expression further.

For the base 2:
\[ \frac{2^{5}}{2^{3}} = 2^{5 - 3} = 2^{2} \]

For the base 7:
\[ \frac{7^{9}}{7^{4}} = 7^{9 - 4} = 7^{5} \]

### Step 4: Combine the results
Now we can combine the results from the previous step:
\[ 2^{2} \times 7^{5} \]

### Final Answer
Thus, the simplified expression in exponential form is:
\[ 2^{2} \times 7^{5} \]

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