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Simplify $a^3 \times a^{-2}.$

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

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

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

Simplify $\large x^8 \div x^2.$

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