Pregunta
Simplify the expression completely: \( \frac{x^{28} \cdot y^{55}}{x^{11} \cdot y^{13}} \) Answer \( = \)
Ask by Wang Ortiz. in the United States
Mar 11,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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The simplified expression is \( x^{17}y^{42} \).
Solución
Calculate or simplify the expression \( \frac{x^{28} \cdot y^{55}}{x^{11} \cdot y^{13}} \).
Simplify the expression by following steps:
- step0: Solution:
\(\frac{x^{28}y^{55}}{x^{11}y^{13}}\)
- step1: Reduce the fraction:
\(\frac{x^{28-11}y^{55}}{y^{13}}\)
- step2: Reduce the fraction:
\(\frac{x^{17}y^{55}}{y^{13}}\)
- step3: Reduce the fraction:
\(\frac{x^{17}y^{55-13}}{1}\)
- step4: Simplify:
\(x^{17}y^{55-13}\)
- step5: Divide the terms:
\(x^{17}y^{42}\)
The simplified expression is \( x^{17}y^{42} \).
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Simplifique esta solución The Deep Dive
To simplify the expression \( \frac{x^{28} \cdot y^{55}}{x^{11} \cdot y^{13}} \), we can apply the laws of exponents. First, we simplify the \( x \) terms: \[ \frac{x^{28}}{x^{11}} = x^{28 - 11} = x^{17}. \] Next, we simplify the \( y \) terms: \[ \frac{y^{55}}{y^{13}} = y^{55 - 13} = y^{42}. \] Combining both results gives us: \[ \frac{x^{28} \cdot y^{55}}{x^{11} \cdot y^{13}} = x^{17} \cdot y^{42}. \] Thus, the fully simplified expression is: \[ \boxed{x^{17} \cdot y^{42}}. \]
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