Here are some challenging exponent simplification problems along with their answers:

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1. Simplify:

$\frac{(x^4y^{-2})^3}{(x^2y^{-3})^2}$

Answer: $x^{8}y$

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2. Simplify:

$\frac{(3x^2y^{-1})^4}{(9x^3y^2)^2}$

Answer: $\frac{1}{3x^2y^8}$

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3. Simplify:

$(2x^{-1}y^3)^2 \cdot (4x^3y^{-1})$

Answer: $16x^5y^5$

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4. Simplify:

$\left(\frac{x^{-2}y^5}{z^{-3}}\right)^2 \cdot \frac{z^4}{x^{-3}y}$

Answer: $\frac{y^{9}z^{10}}{x^7}$

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5. Simplify:

$\frac{(a^{2m}b^{-3n})^4}{(a^{3m}b^{-n})^2}$

Answer: $a^{2m}b^{-10n}$

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Tip:

Always remember to apply the power of a power rule $(a^m)^n = a^{m \cdot n}$ and the division rule $a^m / a^n = a^{m-n}$ when simplifying exponents.

Would you like further clarification or practice on any of these problems?

Related Questions:

1. How does changing the base affect the outcome when simplifying exponents?
2. What happens if negative exponents are present in the denominator?
3. How can you simplify expressions with fractional exponents?
4. How do exponent rules apply when working with scientific notation?
5. What is the relationship between exponents and logarithms?

Let me know if you'd like explanations or new challenges!