Question
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Simplifica. Deja tu respuesta en forma exponencia \( 3^{3} \times 3^{4} \) \( 9^{12} \) \( 9^{7} \)

Ask by Rowe Ball. in the United States
Mar 16,2025

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Tutor-Verified Answer

Answer

\(3^{7}\), \(3^{24}\), \(3^{14}\)

Solution

\(3^{3} \times 3^{4} = 3^{3+4} = 3^{7}\) \(9^{12} = \left(3^2\right)^{12} = 3^{2 \times 12} = 3^{24}\) \(9^{7} = \left(3^2\right)^{7} = 3^{2 \times 7} = 3^{14}\)

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Bonus Knowledge

La expresión \( 3^{3} \times 3^{4} \) se puede simplificar usando la propiedad de los exponentes que dice que al multiplicar potencias con la misma base, se suman los exponentes. Así que, \( 3^{3} \times 3^{4} = 3^{3+4} = 3^{7} \). Ahora, para \( 9^{12} \) y \( 9^{7} \): como \( 9 \) es igual a \( 3^2 \), podemos reescribir estas potencias. Así que \( 9^{12} = (3^2)^{12} = 3^{24} \) y \( 9^{7} = (3^2)^{7} = 3^{14} \). Por lo tanto, tus respuestas simplificadas en forma exponencial son: - \( 3^{7} \) - \( 3^{24} \) - \( 3^{14} \)

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