`9 x^(6) y^(2) ÷ 3x^(3) y =`

Options

A. `3x^(2) y^(2)`
B. `3x^(3) y`
C. `3x^(3) y^(2)`
D. `6x^(3) y`

Answer

To solve the expression \( 9x^6y^2 \div 3x^3y \), we will follow these steps:

### Step 1: Write the expression clearly
We start with the expression:
\[ \frac{9x^6y^2}{3x^3y} \]

### Step 2: Simplify the coefficients
First, we simplify the numerical coefficients (the numbers in front):
\[ \frac{9}{3} = 3 \]
So, we can rewrite the expression as:
\[ 3 \cdot \frac{x^6y^2}{x^3y} \]

### Step 3: Simplify the variable \(x\)
Next, we simplify the \(x\) terms. According to the exponent rule for division, which states that \(a^m \div a^n = a^{m-n}\):
\[ \frac{x^6}{x^3} = x^{6-3} = x^3 \]
So, we have:
\[ 3 \cdot x^3 \cdot \frac{y^2}{y} \]

### Step 4: Simplify the variable \(y\)
Now, we simplify the \(y\) terms using the same exponent rule:
\[ \frac{y^2}{y} = y^{2-1} = y^1 = y \]
Thus, the expression now becomes:
\[ 3x^3y \]

### Final Answer
The final simplified expression is:
\[ 3x^3y \]

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