Pregunta
20. \( \frac{24 x^{-2} y^{4}}{-6 x^{-3} y^{-2} z^{-1}} \)
Ask by Elliott Salazar. in the United States
Jan 30,2025
Solución de tutoría real
Respuesta verificada por el tutor
Responder
\[
-4x y^{6} z
\]
Solución
To simplify the expression:
\[
\frac{24 x^{-2} y^{4}}{-6 x^{-3} y^{-2} z^{-1}}
\]
Follow these steps:
1. **Divide the coefficients:**
\[
\frac{24}{-6} = -4
\]
2. **Simplify the \(x\)-terms using the laws of exponents:**
\[
x^{-2} \div x^{-3} = x^{-2 - (-3)} = x^{1} = x
\]
3. **Simplify the \(y\)-terms:**
\[
y^{4} \div y^{-2} = y^{4 - (-2)} = y^{6}
\]
4. **Simplify the \(z\)-term:**
\[
\frac{1}{z^{-1}} = z^{1} = z
\]
5. **Combine all simplified parts:**
\[
-4 \times x \times y^{6} \times z = -4xy^{6}z
\]
**Final Simplified Expression:**
\[
-4x y^{6} z
\]
Revisado y aprobado por el equipo de tutoría de UpStudy
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To simplify the expression \( \frac{24 x^{-2} y^{4}}{-6 x^{-3} y^{-2} z^{-1}} \), we can break it down step by step. First, simplify the coefficients: \( \frac{24}{-6} = -4 \). Now, let's handle the variables in the numerator and denominator. For \( x \), we have: \[ \frac{x^{-2}}{x^{-3}} = x^{-2 - (-3)} = x^{1} \] For \( y \): \[ \frac{y^{4}}{y^{-2}} = y^{4 - (-2)} = y^{6} \] Lastly, we need to account for \( z \): \[ \frac{1}{z^{-1}} = z^{1} \] Putting everything together, we get: \[ -4 x^{1} y^{6} z^{1} = -4 x y^{6} z \] Thus, the simplified result is: \[ \text{Final answer: } -4 x y^{6} z \]
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