Pregunta
Simplify. \[ \left(-4 u^{4} v\right)^{3} \]
Ask by Higgins Johnson. in the United States
Feb 25,2025
Solución de inteligencia artificial de Upstudy
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\(-64u^{12}v^{3}\)
Solución
Calculate or simplify the expression \( (-4*u^4*v)^3 \).
Simplify the expression by following steps:
- step0: Solution:
\(\left(-4u^{4}v\right)^{3}\)
- step1: Determine the sign:
\(-\left(4u^{4}v\right)^{3}\)
- step2: Use the properties of exponents:
\(-4^{3}\left(u^{4}\right)^{3}v^{3}\)
- step3: Evaluate the power:
\(-64u^{12}v^{3}\)
The simplified form of \((-4u^{4}v)^{3}\) is \(-64u^{12}v^{3}\).
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Simplifique esta solución Beyond the Answer
To simplify the expression \(\left(-4 u^{4} v\right)^{3}\), we first apply the power of a product rule. This means we raise each factor inside the parentheses to the power of 3. 1. Raise \(-4\) to the power of 3: \[ (-4)^{3} = -64 \] 2. Raise \(u^{4}\) to the power of 3: \[ (u^{4})^{3} = u^{12} \] 3. Raise \(v\) to the power of 3: \[ v^{3} = v^{3} \] Now, combine all these results: \[ \left(-4 u^{4} v\right)^{3} = -64 u^{12} v^{3} \] Thus, the simplified expression is: \[ \boxed{-64 u^{12} v^{3}} \]
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