Pregunta
Fully simplify. \[ 16 x^{2} y^{2}\left(-15 x^{5} y^{5}\right) \] Answer Attempt 1 out of 2 Submit Answer
Ask by Cummings Vargas. in the United States
Feb 03,2025
Solución de tutoría real
Respuesta verificada por el tutor
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\[
-240x^{7}y^{7}
\]
Solución
To fully simplify the expression:
\[
16 x^{2} y^{2} \left(-15 x^{5} y^{5}\right)
\]
Follow these steps:
1. **Multiply the coefficients (constants):**
\[
16 \times (-15) = -240
\]
2. **Multiply the \(x\) terms by adding their exponents:**
\[
x^{2} \times x^{5} = x^{2+5} = x^{7}
\]
3. **Multiply the \(y\) terms by adding their exponents:**
\[
y^{2} \times y^{5} = y^{2+5} = y^{7}
\]
4. **Combine all the simplified parts:**
\[
-240 x^{7} y^{7}
\]
**Final Simplified Form:**
\[
-240 x^{7} y^{7}
\]
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Bonus Knowledge
To simplify \( 16 x^{2} y^{2}(-15 x^{5} y^{5}) \), you need to multiply the constants and the variables. First, multiply the numbers: \( 16 \times -15 = -240 \). For the variable \( x \), you add the exponents: \( x^{2} \cdot x^{5} = x^{2+5} = x^{7} \). For the variable \( y \), similarly: \( y^{2} \cdot y^{5} = y^{2+5} = y^{7} \). Putting it all together, the simplified result is: \[ -240 x^{7} y^{7} \]
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