Pregunta
Simplify. \[ \left(5 b^{3} a^{4}\right)^{3} \] Write your answer without parentheses.
Ask by Bradley Schneider. in the United States
Jan 29,2025
Solución de tutoría real
Respuesta verificada por el tutor
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\(125a^{12}b^{9}\)
Solución
To simplify \(\left(5 b^{3} a^{4}\right)^{3}\), apply the exponent to each factor inside the parentheses:
\[
\left(5 b^{3} a^{4}\right)^{3} = 5^{3} \cdot \left(b^{3}\right)^{3} \cdot \left(a^{4}\right)^{3} = 125 \cdot b^{9} \cdot a^{12}
\]
Writing the terms without parentheses and in standard order:
\[
125 a^{12} b^{9}
\]
**Answer:** \(125\,a^{12}\,b^{9}\)
Revisado y aprobado por el equipo de tutoría de UpStudy
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Simplifique esta solución The Deep Dive
To simplify \(\left(5 b^{3} a^{4}\right)^{3}\), we apply the power of a product rule, which states that \((xy)^n = x^n y^n\). First, we take each part: - The coefficient \(5\) raised to the power of \(3\) becomes \(5^3 = 125\). - For \(b^{3}\) raised to the power of \(3\), we multiply the exponents: \(b^{3 \cdot 3} = b^{9}\). - For \(a^{4}\) raised to the power of \(3\), we also multiply the exponents: \(a^{4 \cdot 3} = a^{12}\). Putting it together, we have: \[ \left(5 b^{3} a^{4}\right)^{3} = 125 b^{9} a^{12} \] Thus, the simplified expression is: \[ 125 b^{9} a^{12} \]
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