Question
Upstudy AI Solution
Tutor-Verified Answer
Answer
La expresión simplificada es \( \frac{1}{x^{12}} \).
Solution
Simplify the expression by following steps:
- step0: Solution:
\(\left(x^{4}\times x^{-8}\right)^{3}\)
- step1: Multiply the terms:
\(\left(x^{-4}\right)^{3}\)
- step2: Transform the expression:
\(x^{-4\times 3}\)
- step3: Multiply the numbers:
\(x^{-12}\)
- step4: Simplify:
\(\frac{1}{x^{12}}\)
Para simplificar la expresión \( \left(x^{4} \cdot x^{-8}\right)^{3} \), seguimos estos pasos:
1. **Multiplicación de potencias**: Cuando multiplicamos potencias con la misma base, sumamos los exponentes. Así que:
\[
x^{4} \cdot x^{-8} = x^{4 + (-8)} = x^{-4}
\]
2. **Aplicar la potencia externa**: Ahora elevamos \( x^{-4} \) a la potencia de 3:
\[
(x^{-4})^{3} = x^{-4 \cdot 3} = x^{-12}
\]
3. **Convertir a forma positiva**: Para expresar \( x^{-12} \) en forma positiva, usamos la propiedad de las potencias negativas:
\[
x^{-12} = \frac{1}{x^{12}}
\]
Por lo tanto, la expresión simplificada es:
\[
\frac{1}{x^{12}}
\]
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution The Deep Dive
To simplify \( \left(x^{4} \cdot x^{-8}\right)^{3} \), we start by applying the product of powers rule, which states that when multiplying exponents with the same base, we add the exponents. So, \[ x^{4} \cdot x^{-8} = x^{4 + (-8)} = x^{-4}. \] Now we have \( (x^{-4})^{3} \). According to the power of a power rule, we multiply the exponents: \[ (x^{-4})^{3} = x^{-4 \cdot 3} = x^{-12}. \] Therefore, the final simplified expression is \( x^{-12} \). You can also express it as \( \frac{1}{x^{12}} \) if you prefer to avoid negative exponents!
