Pregunta
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
\( \frac{y^{2}}{x^{2}} \)
Solución
Simplify the expression by following steps:
- step0: Solution:
\(\left(x^{2}y^{-2}\right)^{-1}\)
- step1: Use the properties of exponents:
\(\left(x^{2}\right)^{-1}\left(y^{-2}\right)^{-1}\)
- step2: Evaluate the power:
\(x^{-2}y^{2}\)
- step3: Simplify:
\(\frac{y^{2}}{x^{2}}\)
To simplify the expression \( \left(x^{2} y^{-2}\right)^{-1} \), we can follow these steps:
1. **Apply the negative exponent rule**: The rule states that \( a^{-n} = \frac{1}{a^n} \). Therefore, we can rewrite the expression as:
\[
\left(x^{2} y^{-2}\right)^{-1} = \frac{1}{x^{2} y^{-2}}
\]
2. **Simplify the denominator**: The term \( y^{-2} \) can be rewritten as \( \frac{1}{y^{2}} \). Thus, we have:
\[
x^{2} y^{-2} = x^{2} \cdot \frac{1}{y^{2}} = \frac{x^{2}}{y^{2}}
\]
3. **Substituting back into the expression**: Now we can substitute this back into our expression:
\[
\frac{1}{x^{2} y^{-2}} = \frac{1}{\frac{x^{2}}{y^{2}}} = \frac{y^{2}}{x^{2}}
\]
Thus, the simplified form of \( \left(x^{2} y^{-2}\right)^{-1} \) is:
\[
\frac{y^{2}}{x^{2}}
\]
Respondido por UpStudy AI y revisado por un tutor profesional
Como
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Mind Expander
To simplify \( \left(x^{2} y^{-2}\right)^{-1} \), we apply the rule that states \( (a^m)^{-n} = a^{-m} \). Thus, we can distribute the exponent -1 across the terms inside the parentheses: \[ \left(x^{2} y^{-2}\right)^{-1} = x^{-2} y^{2} \] Rearranging to a more conventional form, we can express this as: \[ \frac{y^{2}}{x^{2}} \] And that's the simplified version!

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