Pregunta
\begin{tabular}{l}\( 1 \leftarrow \begin{array}{l}\text { Simplify the expression. Write the result us } \\ \text { equal to } 0\end{array} \) \\ \( \frac{x^{2} x^{8}}{x^{4}} \) \\ \hline\end{tabular}
Ask by Matthews Edwards. in the United States
Jan 27,2025
Solución de tutoría real
Respuesta verificada por el tutor
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\( x^{6} = 0 \)
Solución
To simplify the expression \(\frac{x^{2} x^{8}}{x^{4}}\) and set it equal to 0, follow these steps:
1. **Combine the exponents in the numerator:**
\[
x^{2} \times x^{8} = x^{2+8} = x^{10}
\]
2. **Divide by \(x^{4}\):**
\[
\frac{x^{10}}{x^{4}} = x^{10-4} = x^{6}
\]
3. **Set the simplified expression equal to 0:**
\[
x^{6} = 0
\]
**Final Result:**
\[
x^{6} = 0
\]
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Beyond the Answer
To simplify the expression \(\frac{x^{2} x^{8}}{x^{4}}\), first combine the numerators: \(x^{2} \cdot x^{8} = x^{10}\). Now, the expression looks like \(\frac{x^{10}}{x^{4}}\). When dividing powers with the same base, subtract the exponent in the denominator from the exponent in the numerator, so \(x^{10 - 4} = x^{6}\). Thus, the simplified expression is \(x^{6} = 0\). To solve \(x^{6} = 0\), we note that the only value of \(x\) that satisfies this equation is \(x = 0\). So, we've simplified the expression and found the solution!
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