Match the correct steps to simplify the expression: 4x(3)⋅3x(2)/6x

Question

(4 points)
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

responses
x(6)
x(5)
12
1
7
x(4)
6x(4)
2x(4)
7x(5)/6
2x(5)

Answer 1

To simplify the expression \( \frac{4x^3 \cdot 3x^2}{6x} \), we will follow the correct steps outlined.

Step 1 - Simplify the exponent in the numerator:

Combine the exponents in the numerator:

• \(x^3 \cdot x^2 = x^{3+2} = x^5\)
• The numerator becomes \( 4 \cdot 3 \cdot x^5 = 12x^5\).

Response: 12x(5)

Step 2 - Simplify the coefficient in the numerator:

Now we have \( \frac{12x^5}{6x} \). Simplify the coefficient:

• \( \frac{12}{6} = 2 \).

So it becomes \( \frac{2x^5}{x} \).

Response: 2x(5)

Step 3 - Simplify the exponent from numerator and denominator:

Now simplify the x's:

• \( \frac{x^5}{x} = x^{5-1} = x^4 \).

Now the expression is \( 2x^4 \).

Response: 2x(4)

Step 4 - Reduce and write the complete answer:

Thus, the complete simplified expression is \( 2x^4 \).

Response: 2x(4) (already noted in the previous step)

So the responses chosen for each step would be:

1. 12x(5)
2. 2x(5)
3. 2x(4)
4. 2x(4) (this is the final answer as well)

To summarize the matching:

• Step 1: 12x(5)
• Step 2: 2x(5)
• Step 3: x(4)
• Step 4: 2x(4)