SIMPLIFY $$ \left(x^{2} y^{-2}\right)^{-1} $$

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UpStudy AI · Accepted Answer

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:
$$
\frac{y^{2}}{x^{2}}
$$
$$ \frac{y^{2}}{x^{2}} $$

SIMPLIFY \( \left(x^{2} y^{-2}\right)^{-1} \)

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