Simplify `486 b ^(3) x ^(2) a ^(4) z ^(3)//27 a ^(3) b ^(2)z`

Options

A. `18 bx ^(2) az ^(2)`
B. `18 bx ^(2) a ^(2)z`
C. `36 ba ^(2) z`
D. `36 bxa ^(2) z`

Answer

To simplify the expression \( \frac{486 b^3 x^2 a^4 z^3}{27 a^3 b^2 z} \), we will follow these steps:

### Step 1: Simplify the numeric coefficients
First, we simplify the numeric coefficients \( \frac{486}{27} \).

\[ \frac{486}{27} = 18 \]

### Step 2: Simplify the variable \( a \)
Next, we simplify the \( a \) terms. We have \( a^4 \) in the numerator and \( a^3 \) in the denominator.

\[ \frac{a^4}{a^3} = a^{4-3} = a^1 = a \]

### Step 3: Simplify the variable \( b \)
Now, we simplify the \( b \) terms. We have \( b^3 \) in the numerator and \( b^2 \) in the denominator.

\[ \frac{b^3}{b^2} = b^{3-2} = b^1 = b \]

### Step 4: Simplify the variable \( z \)
Next, we simplify the \( z \) terms. We have \( z^3 \) in the numerator and \( z^1 \) in the denominator.

\[ \frac{z^3}{z^1} = z^{3-1} = z^{2} \]

### Step 5: Combine all the simplified parts
Now, we combine all the simplified parts together:

\[ \frac{486 b^3 x^2 a^4 z^3}{27 a^3 b^2 z} = 18 a b x^2 z^2 \]

### Final Result
Thus, the simplified expression is:

\[ 18 a b x^2 z^2 \]

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