Simplify and write the answer in exponential
`(2^(8)xx a^(5))/(4^(3)xx a^(3))`

Answer

To simplify the expression \((2^{8} \times a^{5}) / (4^{3} \times a^{3})\) and write the answer in exponential form, we can follow these steps:

### Step 1: Rewrite the expression
The expression can be rewritten as:
\[ \frac{2^{8} \times a^{5}}{4^{3} \times a^{3}} \]

### Step 2: Express \(4^{3}\) in terms of base \(2\)
Since \(4\) can be expressed as \(2^{2}\), we can rewrite \(4^{3}\) as:
\[ 4^{3} = (2^{2})^{3} = 2^{2 \times 3} = 2^{6} \]
Now substitute this back into the expression:
\[ \frac{2^{8} \times a^{5}}{2^{6} \times a^{3}} \]

### Step 3: Simplify the expression using properties of exponents
Using the property \(\frac{a^{m}}{a^{n}} = a^{m-n}\), we can simplify both the \(2\) and \(a\) terms:
\[ \frac{2^{8}}{2^{6}} = 2^{8-6} = 2^{2} \]
\[ \frac{a^{5}}{a^{3}} = a^{5-3} = a^{2} \]
Now, we can combine these results:
\[ 2^{2} \times a^{2} \]

### Step 4: Write the final answer in exponential form
The final simplified expression is:
\[ 2^{2} \times a^{2} = (2a)^{2} \]

### Final Answer:
\[ (2a)^{2} \]

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