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Combine your skills of working with exponents and manipulating expressions for radical glory.

Simplify \( a^3 \times a^{-2}.\)

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Simplify \( \left( x^3 \right)^2 \).

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Simplify \( \left( -3 x^3 \right)^2 \).

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Simplify \[ (x^2 y)^3 \times \left( \frac{y}{x} \right)^2 \div (-xy). \]

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Simplify \[ \large x^8 \div x^2. \]

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