Pregunta
Multiply. \[ -2 x^{3}\left(-x^{3}\right) \] Simplify your answer as much as possible.
Ask by Simmons Schneider. in the United States
Jan 24,2025
Solución de tutoría real
Respuesta verificada por el tutor
Responder
The simplified answer is \(2x^{6}\).
Solución
Certainly! Let's multiply and simplify the expression step by step.
**Given Expression:**
\[
-2x^{3} \cdot (-x^{3})
\]
**Step 1: Multiply the Coefficients**
\[
-2 \times (-1) = 2
\]
Multiplying two negative numbers results in a positive number.
**Step 2: Multiply the Variables with Exponents**
\[
x^{3} \times x^{3} = x^{3+3} = x^{6}
\]
When multiplying like bases, you add the exponents.
**Step 3: Combine the Results**
\[
2 \times x^{6} = 2x^{6}
\]
**Final Simplified Expression:**
\[
2x^{6}
\]
So, the simplified form of \(-2x^{3} \cdot (-x^{3})\) is **\(2x^{6}\)**.
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Extra Insights
To multiply the expression \(-2x^{3}(-x^{3})\), we start by multiplying the coefficients and the variable parts separately. First, multiply the coefficients: \(-2 \times -1 = 2\). Next, for the variable parts, we apply the law of exponents: \[ x^{3} \cdot x^{3} = x^{3+3} = x^{6}. \] Now, combine both parts: \[ 2x^{6}. \] So, the simplified answer is: \[ \boxed{2x^{6}}. \]
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