To simplify this expression, let's break it down step by step:
1. First, let's simplify the term (x^-2)^-1. When we raise a power to another power, we multiply the exponents. So (x^-2)^-1 becomes x^2.
2. Next, let's simplify x^-1. Any number or variable raised to the power of -1 is equal to its reciprocal. So x^-1 becomes 1/x.
3. Next, let's simplify x^-1 again. Similarly, x^-1 becomes 1/x.
4. Now, let's simplify (1/x) * (1/x). When we multiply two fractions, we simply multiply the numerators together and the denominators together. So (1/x) * (1/x) becomes 1/(x*x), which simplifies to 1/x^2.
5. Finally, let's divide 1/x^2 by x^2. When we divide two fractions, we multiply the first fraction by the reciprocal of the second fraction. So 1/x^2 divided by x^2 becomes (1/x^2) * (1/x^2). This can be written as 1/(x^2 * x^2), which simplifies to 1/x^4.
Therefore, the simplified expression is 1/x^4.
(x^-2)^-1x ^-1 x^-1/x^2
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