Question
0) \( \frac{1}{2} p^{8} \cdot 8 q^{5} \cdot \frac{r^{4}}{4 p^{4} q} \)
Ask by Deleon Reese. in Brazil
Feb 28,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
A expressão simplificada é \( p^{4} \cdot q^{4} \cdot r^{4} \).
Solution
Vamos simplificar a expressão:
(1/2)·p⁸ · 8·q⁵ · (r⁴/(4·p⁴·q))
1) Agrupando os coeficientes:
(1/2)·8·(1/4) = (8/2)·(1/4) = 4/4 = 1
2) Agora, os termos com p:
p⁸ / p⁴ = p^(8−4) = p⁴
3) Em seguida, os termos com q:
q⁵ / q = q^(5−1) = q⁴
4) E o termo com r permanece:
r⁴
Assim, a expressão simplificada é:
p⁴ · q⁴ · r⁴
Portanto, o resultado final é: p⁴·q⁴·r⁴.
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Simplify this solution Extra Insights
To simplify the expression \( \frac{1}{2} p^{8} \cdot 8 q^{5} \cdot \frac{r^{4}}{4 p^{4} q} \), we first address each component step-by-step. 1. **Combine the constants**: \[ \frac{1}{2} \cdot 8 \cdot \frac{1}{4} = \frac{8}{8} = 1 \] 2. **Combine the powers of \( p \)**: \[ p^{8} \cdot \frac{1}{p^{4}} = p^{8-4} = p^{4} \] 3. **Combine the powers of \( q \)**: \[ q^{5} \cdot \frac{1}{q} = q^{5-1} = q^{4} \] Now, putting all this together, we have: \[ 1 \cdot p^{4} \cdot q^{4} \cdot r^{4} = p^{4} q^{4} r^{4} \] So, the simplified expression is: \[ p^{4} q^{4} r^{4} \]
