Question

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

Answer 1

To simplify the expression \( \frac{4x^3 \cdot 3x^2}{6x} \), the correct steps are as follows:

**Step 1:** Simplify the exponent in the numerator.

Here, we have \( x^3 \cdot x^2 \), which simplifies to \( x^{3+2} = x^5 \).

**Step 2:** Simplify the coefficient in the numerator.

Multiply the coefficients: \( 4 \cdot 3 = 12 \).

**Step 3:** Simplify the exponent from numerator and denominator.

Now we have \( \frac{12x^5}{6x} \). To simplify, we subtract the exponent in the denominator from the exponent in the numerator: \( x^{5-1} = x^4 \).

**Step 4:** Reduce and write the complete answer.

Now simplify the coefficient: \( \frac{12}{6} = 2 \). So the final answer is \( 2x^4 \).

Here’s the order of the steps matched correctly:

- 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