Pregunta
Simplify. \[ \left(\frac{-3 x}{y^{3}}\right)^{4} \] Write your answer without parentheses.
Ask by Kirk Moreno. in the United States
Mar 14,2025
Solución de inteligencia artificial de Upstudy
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\(\frac{81x^{4}}{y^{12}}\)
Solución
Calculate or simplify the expression \( \left(\frac{-3x}{y^{3}}\right)^{4} \).
Simplify the expression by following steps:
- step0: Solution:
\(\left(\frac{-3x}{y^{3}}\right)^{4}\)
- step1: Divide the terms:
\(\left(-\frac{3x}{y^{3}}\right)^{4}\)
- step2: Rewrite the expression:
\(\frac{\left(3x\right)^{4}}{\left(y^{3}\right)^{4}}\)
- step3: Evaluate the power:
\(\frac{81x^{4}}{y^{12}}\)
The simplified form of the expression \(\left(\frac{-3x}{y^{3}}\right)^{4}\) is \(\frac{81x^{4}}{y^{12}}\).
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Simplifique esta solución Bonus Knowledge
To simplify the expression \(\left(\frac{-3 x}{y^{3}}\right)^{4}\), we will raise both the numerator and the denominator inside the parentheses to the power of 4. First, we raise the numerator: \[ (-3 x)^{4} = (-3)^{4} \cdot x^{4} = 81 x^{4}. \] Next, we raise the denominator: \[ (y^{3})^{4} = y^{3 \cdot 4} = y^{12}. \] Now we can combine these results: \[ \left(\frac{-3 x}{y^{3}}\right)^{4} = \frac{81 x^{4}}{y^{12}}. \] The final simplified expression is: \[ \frac{81 x^{4}}{y^{12}}. \]
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