The product of `4a^(2),-6b^(2) and 3a^(2)b^(2)` is

Options

A. `a^(2)b^(2)`
B. `13a^(4)b^(4)`
C. `-72a^(4)b^(4)`
D. `a^(4)b^(4)`

Answer

To find the product of the expressions \(4a^2\), \(-6b^2\), and \(3a^2b^2\), we will multiply them step by step.

### Step 1: Write the expression
We start with the expression:
\[ 4a^2 \times (-6b^2) \times (3a^2b^2) \]

### Step 2: Multiply the coefficients
First, we multiply the numerical coefficients:
\[ 4 \times (-6) \times 3 \]
Calculating this step-by-step:
- \(4 \times (-6) = -24\)
- Now, \(-24 \times 3 = -72\)

So, the product of the coefficients is \(-72\).

### Step 3: Multiply the \(a\) terms
Next, we multiply the \(a\) terms:
\[ a^2 \times a^2 \]
Using the property of exponents, we add the exponents:
\[ a^{2+2} = a^4 \]

### Step 4: Multiply the \(b\) terms
Now, we multiply the \(b\) terms:
\[ b^2 \times b^2 \]
Again, using the property of exponents:
\[ b^{2+2} = b^4 \]

### Step 5: Combine all parts
Now we combine all the parts together:
\[ -72 \times a^4 \times b^4 = -72a^4b^4 \]

### Final Answer
The product of \(4a^2\), \(-6b^2\), and \(3a^2b^2\) is:
\[ \boxed{-72a^4b^4} \]