Carter Evans
11/16/2023 · Junior High School
resuelve aplicensiso Propiesandes A) \( (-5)^{3}(-5)^{4}:(-5)^{5}= \)
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Tutor-Verified Answer
Step-by-step Solution
Para resolver la expresión \( (-5)^{3}(-5)^{4}:(-5)^{5} \), podemos aplicar las propiedades de las potencias.
1. **Multiplicación de potencias con la misma base**: \( a^m \cdot a^n = a^{m+n} \)
2. **División de potencias con la misma base**: \( \frac{a^m}{a^n} = a^{m-n} \)
Siguiendo estos pasos:
Primero, multiplicamos las potencias:
\[
(-5)^{3} \cdot (-5)^{4} = (-5)^{3+4} = (-5)^{7}
\]
Ahora, sustituimos esto en la expresión original:
\[
(-5)^{7} : (-5)^{5}
\]
Ahora aplicamos la propiedad de la división de potencias:
\[
\frac{(-5)^{7}}{(-5)^{5}} = (-5)^{7-5} = (-5)^{2}
\]
Finalmente, calculamos \( (-5)^{2} \):
\[
(-5)^{2} = 25
\]
Por lo tanto, el resultado de la expresión \( (-5)^{3}(-5)^{4}:(-5)^{5} \) es:
\[
\boxed{25}
\]
Quick Answer
El resultado de la expresión es 25.
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