Simplify `(3x^5y^3z^2)/(x^2yz^4)xxx^3y^3z`

Options

A. `3x^8y^6z^2`
B. `(3x^4)/(z^3)`
C. `(3x^3y^2)/(z^3)`
D. `(3x^6y^5)/(z^2)`

Answer

To simplify the expression \((3x^5y^3z^2)/(x^2yz^4) \cdot (x^3y^3z)\), we will follow these steps:

### Step 1: Rewrite the expression
We start with the expression:
\[ \frac{3x^5y^3z^2}{x^2yz^4} \cdot (x^3y^3z) \]
This can be rewritten as:
\[ \frac{3x^5y^3z^2 \cdot x^3y^3z}{x^2yz^4} \]

### Step 2: Combine the numerators
Now, we will multiply the terms in the numerator:
\[ 3x^5y^3z^2 \cdot x^3y^3z = 3 \cdot x^{5+3} \cdot y^{3+3} \cdot z^{2+1} = 3x^8y^6z^3 \]

### Step 3: Write the new expression
Now, we have:
\[ \frac{3x^8y^6z^3}{x^2yz^4} \]

### Step 4: Simplify the fraction
Next, we will simplify the fraction by dividing the powers of \(x\), \(y\), and \(z\):
- For \(x\): \(x^{8-2} = x^6\)
- For \(y\): \(y^{6-1} = y^5\)
- For \(z\): \(z^{3-4} = z^{-1}\)

Putting it all together, we have:
\[ 3x^6y^5z^{-1} \]

### Step 5: Rewrite with positive exponents
Since \(z^{-1} = \frac{1}{z}\), we can rewrite the expression as:
\[ \frac{3x^6y^5}{z} \]

### Final Answer
Thus, the simplified expression is:
\[ \frac{3x^6y^5}{z} \]

---