Simplify `576b ^(3) x ^(2) a ^(4) z ^(3)//36a ^(3) b ^()z`

Options

A. `16 bx ^(2) az ^(2)`
B. `8bx ^(2) a ^(2)z`
C. `32ba ^(2)z`
D. `32bxa ^(2)z`

Answer

To simplify the expression \( \frac{576b^3x^2a^4z^3}{36a^3bz} \), we will follow these steps:

### Step 1: Simplify the coefficients
First, we simplify the numerical coefficients \( \frac{576}{36} \).

\[ 576 \div 36 = 16 \]

### Step 2: Simplify the variables
Next, we simplify the variables in the expression. We will handle each variable separately.

- For \( b \):
\[ b^3 \div b = b^{3-1} = b^2 \]

- For \( a \):
\[ a^4 \div a^3 = a^{4-3} = a^1 = a \]

- For \( z \):
\[ z^3 \div z = z^{3-1} = z^2 \]

### Step 3: Combine the simplified parts
Now we can combine the simplified coefficients and variables:

\[ \text{Numerator: } 16b^2x^2a z^2 \]

Thus, the simplified expression is:

\[ 16b^2x^2az^2 \]

### Final Answer:
\[ \frac{576b^3x^2a^4z^3}{36a^3bz} = 16b^2x^2az^2 \]

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