The value of ` (-27 x ^(2) y)div (- 9 xy )` is

Options

A. `3 xy`
B. `- 3 xy`
C. `- 3x`
D. `3x`

Answer

To solve the expression \((-27 x^2 y) \div (-9 xy)\), we will follow these steps:

### Step 1: Write the expression in fraction form
We can express the division as a fraction:
\[ \frac{-27 x^2 y}{-9 xy} \]

### Step 2: Cancel out the negative signs
Since both the numerator and the denominator have a negative sign, they will cancel each other out:
\[ \frac{27 x^2 y}{9 xy} \]

### Step 3: Simplify the coefficients
Now, we can simplify the coefficients (the numerical parts) of the fraction:
\[ \frac{27}{9} = 3 \]
So, we rewrite the expression as:
\[ 3 \cdot \frac{x^2 y}{xy} \]

### Step 4: Simplify the variables
Next, we simplify the variable part \(\frac{x^2 y}{xy}\):
- The \(y\) in the numerator and denominator cancels out.
- For the \(x\) terms, we have \(x^2\) in the numerator and \(x\) in the denominator, which simplifies to \(x^{2-1} = x\).

Thus, we have:
\[ 3 \cdot x = 3x \]

### Final Answer
The value of \((-27 x^2 y) \div (-9 xy)\) is:
\[ 3x \]

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