Pregunta
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\[
\frac{2^{-2}}{3^{2}} = \frac{1}{36} \approx 0.02778
\]
Solución
To simplify the expression \( \frac{2^{-2}}{3^{2}} \), follow these steps:
1. **Understand Negative Exponents:**
A negative exponent indicates the reciprocal of the base raised to the positive exponent. In general:
\[
a^{-n} = \frac{1}{a^{n}}
\]
2. **Apply the Rule to \( 2^{-2} \):**
\[
2^{-2} = \frac{1}{2^{2}} = \frac{1}{4}
\]
3. **Compute \( 3^{2} \):**
\[
3^{2} = 9
\]
4. **Substitute Back into the Original Expression:**
\[
\frac{2^{-2}}{3^{2}} = \frac{\frac{1}{4}}{9}
\]
5. **Simplify the Division of Fractions:**
Dividing by a number is the same as multiplying by its reciprocal:
\[
\frac{\frac{1}{4}}{9} = \frac{1}{4} \times \frac{1}{9} = \frac{1}{36}
\]
6. **Final Answer:**
\[
\frac{2^{-2}}{3^{2}} = \frac{1}{36}
\]
If you prefer a decimal representation:
\[
\frac{1}{36} \approx 0.02778
\]
**Summary:**
\[
\frac{2^{-2}}{3^{2}} = \frac{1}{36} \approx 0.02778
\]
Revisado y aprobado por el equipo de tutoría de UpStudy
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Simplifique esta solución Extra Insights
Let's simplify the expression \( \frac{2^{-2}}{3^{2}} \). First, we can break it down: \( 2^{-2} \) is equal to \( \frac{1}{2^2} \), which simplifies to \( \frac{1}{4} \). Now, \( 3^2 \) equals \( 9 \). So we have \( \frac{2^{-2}}{3^2} = \frac{\frac{1}{4}}{9} = \frac{1}{4 \times 9} = \frac{1}{36} \). Thus, the final answer is \( \frac{1}{36} \). This expression shows how negative exponents can help simplify fractions, reminding us to flip them to their positive counterparts!
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