Question

Match the correct steps to simplify the expression: 4 x superscript 3⋅3 x superscript2/6x
(4 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
Step 1 - simplify the exponent in the numerator
Step 2 - Simplify the coefficient in the numerator
Step 3 - Simplify the exponent from numerator and denominator
Step 4 - Reduce and write the complete answer
Skip to navigation

options: x superscript6, x superscript5, 12, 1, 7, x superscript4, 6 x superscript4, 2 x superscript4, 7 x superscript5/6, 2 x superscript5

Answer 1

To simplify the expression \( \frac{4 x^3 \cdot 3 x^2}{6 x} \), we can follow these steps:

### Step 1 - Simplify the exponent in the numerator
- Combine the exponents of \( x \) in the numerator:
\[
x^3 \cdot x^2 = x^{3 + 2} = x^5
\]
So, we get:
\[
4 \cdot 3 \cdot x^5 = 12 x^5
\]

### Step 2 - Simplify the coefficient in the numerator
- Coefficients:
\[
\frac{12}{6} = 2
\]

### Step 3 - Simplify the exponent from numerator and denominator
- Now we have:
\[
\frac{2 x^5}{x} = 2 x^{5 - 1} = 2 x^4
\]

### Step 4 - Reduce and write the complete answer
- The final simplified expression is:
\[
2 x^4
\]

Now, inserting the correct responses into the respective steps:

1. **Step 1 - simplify the exponent in the numerator**: **x^5**
2. **Step 2 - simplify the coefficient in the numerator**: **12**
3. **Step 3 - simplify the exponent from numerator and denominator**: **x^4**
4. **Step 4 - reduce and write the complete answer**: **2 x^4**

The matches are:
1. Step 1 - x^5
2. Step 2 - 12
3. Step 3 - x^4
4. Step 4 - 2 x^4