Pregunta
Simplify \( \left(y^{3}\right)^{5} \cdot y^{4} \) \( O y^{19} \) \( O y^{60} \) \( y^{12} \) \( y^{32} \)
Ask by Hills Gray. in the United States
Feb 28,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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The simplified expression is \( y^{19} \).
Solución
To simplify (y³)⁵ · y⁴, follow these steps:
1. First, apply the power rule: (y³)⁵ = y^(3·5) = y¹⁵.
2. Then, multiply y¹⁵ by y⁴. When multiplying like bases, add the exponents: y¹⁵ · y⁴ = y^(15+4) = y¹⁹.
Thus, the simplified expression is y¹⁹.
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Simplifique esta solución The Deep Dive
When simplifying the expression \( \left(y^{3}\right)^{5} \cdot y^{4} \), we can first apply the power of a power rule. This states that \( (a^m)^n = a^{m \cdot n} \). So, \( \left(y^{3}\right)^{5} \) simplifies to \( y^{15} \). Now we combine it with \( y^{4} \): \[ y^{15} \cdot y^{4} = y^{15 + 4} = y^{19} \] So, the simplified result is \( y^{19} \).
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