Question
Match the correct steps to simplify the expression: 4x to the third power times 3x to the second power divided by 6x
Answers
Answered by
GPT-4o mini
To simplify the expression \( \frac{4x^3 \cdot 3x^2}{6x} \), follow these steps:
1. **Multiply the Numerator**: Multiply \( 4x^3 \) and \( 3x^2 \).
- \( 4 \cdot 3 = 12 \)
- \( x^3 \cdot x^2 = x^{3+2} = x^5 \)
- So, \( 4x^3 \cdot 3x^2 = 12x^5 \).
2. **Formulate the Expression**: Rewrite the fraction using the result from step 1:
\[
\frac{12x^5}{6x}
\]
3. **Simplify the Coefficients**: Divide the coefficients:
- \( \frac{12}{6} = 2 \)
4. **Simplify the Variable Part**: Divide the powers of \( x \):
- \( \frac{x^5}{x} = x^{5-1} = x^4 \)
5. **Combine Results**: Combine the simplified coefficient and variable part:
\[
2x^4
\]
The simplified expression is:
\[
2x^4
\]
1. **Multiply the Numerator**: Multiply \( 4x^3 \) and \( 3x^2 \).
- \( 4 \cdot 3 = 12 \)
- \( x^3 \cdot x^2 = x^{3+2} = x^5 \)
- So, \( 4x^3 \cdot 3x^2 = 12x^5 \).
2. **Formulate the Expression**: Rewrite the fraction using the result from step 1:
\[
\frac{12x^5}{6x}
\]
3. **Simplify the Coefficients**: Divide the coefficients:
- \( \frac{12}{6} = 2 \)
4. **Simplify the Variable Part**: Divide the powers of \( x \):
- \( \frac{x^5}{x} = x^{5-1} = x^4 \)
5. **Combine Results**: Combine the simplified coefficient and variable part:
\[
2x^4
\]
The simplified expression is:
\[
2x^4
\]