Here are some moderate-level exponent simplification problems with their answers directly underneath:

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1. Simplify:

$(3^2 \cdot 3^4)^3$

Answer:
$(3^2 \cdot 3^4)^3 = 3^{(2+4)\cdot 3} = 3^{18}$

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2. Simplify:

$\frac{(x^5)^3}{x^4 \cdot x^2}$

Answer:
$\frac{(x^5)^3}{x^4 \cdot x^2} = \frac{x^{15}}{x^{4+2}} = x^{15-6} = x^9$

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3. Simplify:

$(2^3 \cdot 5^2)^2 \div 2^4$

Answer:
$(2^3 \cdot 5^2)^2 \div 2^4 = (2^{3\cdot2} \cdot 5^{2\cdot2}) \div 2^4 = 2^6 \cdot 5^4 \div 2^4 = 2^{6-4} \cdot 5^4 = 2^2 \cdot 5^4$

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4. Simplify:

$(xy^2)^4 \cdot (x^3y)^2$

Answer:
$(xy^2)^4 \cdot (x^3y)^2 = x^4y^{8} \cdot x^{6}y^2 = x^{4+6}y^{8+2} = x^{10}y^{10}$

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5. Simplify:

$\left(\frac{a^3}{b^2}\right)^4 \cdot \frac{b^8}{a^5}$

Answer:
$\left(\frac{a^3}{b^2}\right)^4 \cdot \frac{b^8}{a^5} = \frac{a^{3\cdot4}}{b^{2\cdot4}} \cdot \frac{b^8}{a^5} = \frac{a^{12}}{b^8} \cdot \frac{b^8}{a^5} = \frac{a^{12-5}}{b^{8-8}} = \frac{a^7}{1} = a^7$

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Do you want more practice problems or a deeper explanation of any of these steps? 😊

Related Questions:

1. How do exponent rules apply to simplifying fractions involving powers?
2. What is the difference between multiplying and dividing exponents with the same base?
3. How can exponents be combined with roots for simplification?
4. What are common pitfalls when simplifying expressions with multiple bases?
5. Can exponent rules be applied to variables and constants interchangeably?

Tip: Always group terms with the same base and carefully apply rules step by step to avoid errors.