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The given expression is \(\left(\frac{1}{x^2}\right)^4\).

To simplify this expression, we can use the power of a quotient rule, which states that:

\[
\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}
\]

Applying this to \(\left(\frac{1}{x^2}\right)^4\):

\[
\left(\frac{1}{x^2}\right)^4 = \frac{1^4}{(x^2)^4} = \frac{1}{x^{2 \cdot 4}} = \frac{1}{x^8}
\]

Thus, the simplified expression is:

\[
\frac{1}{x^8}
\]

Would you like further details or explanations on any part of this? Here are some related questions you might find useful:

1. How does the power of a quotient rule work for more complex fractions?
2. What happens when negative exponents are introduced into such expressions?
3. Can you explain the difference between product of powers and power of a power rule?
4. How do we simplify expressions involving fractional exponents?
5. What are some common mistakes when applying exponent rules?

**Tip**: When dealing with exponents, always check if there are rules like product, quotient, or power rules that can simplify the expression quickly.

Learn how to simplify the exponential expression (1 / x^2)^4 using the power of a quotient rule. This problem explores exponent rules, applying them step-by-step to arrive at the simplified form 1 / x^8. Ideal for students in Grades 8-10.

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