Simplify and express each of the following in exponential form:
`(4^(5)xxa^(8)b^3)/(4^(5)xxa^(5)b^2)`

Answer

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

### Step 1: Write the expression clearly
We start with the expression:
\[ \frac{4^{5} \cdot a^{8} \cdot b^{3}}{4^{5} \cdot a^{5} \cdot b^{2}} \]

### Step 2: Simplify the base 4 terms
Using the property of exponents that states \(\frac{p^{m}}{p^{n}} = p^{m-n}\), we can simplify the \(4^{5}\) terms:
\[ \frac{4^{5}}{4^{5}} = 4^{5-5} = 4^{0} \]

### Step 3: Simplify the \(a\) terms
Next, we simplify the \(a\) terms:
\[ \frac{a^{8}}{a^{5}} = a^{8-5} = a^{3} \]

### Step 4: Simplify the \(b\) terms
Now, we simplify the \(b\) terms:
\[ \frac{b^{3}}{b^{2}} = b^{3-2} = b^{1} \]

### Step 5: Combine the simplified terms
Now we can combine all the simplified parts together:
\[ 4^{0} \cdot a^{3} \cdot b^{1} \]

### Step 6: Apply the property of zero exponent
Since \(4^{0} = 1\), we can simplify further:
\[ 1 \cdot a^{3} \cdot b^{1} = a^{3} \cdot b \]

### Final Answer
Thus, the simplified expression in exponential form is:
\[ a^{3} \cdot b \]