Simplify and express each of the following in exponential form:
`(2^(3)xx3^(4)xx4)/(3xx32)`

Answer

To simplify the expression \( \frac{2^3 \times 3^4 \times 4}{3 \times 32} \) and express it in exponential form, we can follow these steps:

### Step 1: Rewrite the numbers in exponential form
First, we need to express all numbers in the equation using exponents. We know that:
- \( 4 = 2^2 \)
- \( 32 = 2^5 \)

So we can rewrite the expression as:
\[ \frac{2^3 \times 3^4 \times 2^2}{3 \times 2^5} \]

### Step 2: Combine the terms in the numerator
Now, we can combine the powers of \( 2 \) in the numerator:
\[ 2^3 \times 2^2 = 2^{3+2} = 2^5 \]

Thus, the expression now looks like:
\[ \frac{2^5 \times 3^4}{3 \times 2^5} \]

### Step 3: Rewrite the denominator
We can express \( 3 \) in the denominator as \( 3^1 \):
\[ \frac{2^5 \times 3^4}{3^1 \times 2^5} \]

### Step 4: Simplify the expression
Now we can simplify the expression by canceling out \( 2^5 \) from the numerator and the denominator:
\[ \frac{3^4}{3^1} \]

Using the property of exponents \( \frac{a^m}{a^n} = a^{m-n} \), we can simplify further:
\[ 3^{4-1} = 3^3 \]

### Step 5: Final result
Thus, the simplified expression in exponential form is:
\[ 3^3 \]