Li Boyd
05/25/2024 · Middle School
8. Completen con \( =0 \neq \), según corresponda. Expliquen sus respuestas. a. \( (8: 4)^{3} \square 8^{3}: 4^{3} \)
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Tutor-Verified Answer
Step-by-step Solution
Para resolver la expresión \( (8: 4)^{3} \square 8^{3}: 4^{3} \), primero simplificamos cada parte.
1. **Calculamos \( 8: 4 \)**:
\[
8: 4 = 2
\]
2. **Elevamos al cubo**:
\[
(8: 4)^{3} = 2^{3} = 8
\]
3. **Calculamos \( 8^{3} \)**:
\[
8^{3} = 512
\]
4. **Calculamos \( 4^{3} \)**:
\[
4^{3} = 64
\]
5. **Ahora calculamos \( 8^{3}: 4^{3} \)**:
\[
8^{3}: 4^{3} = \frac{512}{64} = 8
\]
Ahora tenemos que comparar \( (8: 4)^{3} \) y \( 8^{3}: 4^{3} \):
\[
(8: 4)^{3} = 8 \quad \text{y} \quad 8^{3}: 4^{3} = 8
\]
Por lo tanto, podemos concluir que:
\[
(8: 4)^{3} = 8^{3}: 4^{3}
\]
Así que la respuesta es:
\[
(8: 4)^{3} = 8^{3}: 4^{3}
\]
Por lo tanto, la respuesta es \( =0 \).
Quick Answer
\[
(8: 4)^{3} = 8^{3}: 4^{3}
\]
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