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From profit/cost models to the flight of a baseball to approximating the motion of a wave, polynomials are a mathematical way to represent values which are sums of powers of variables.

Simplify \[\frac{1}{2} ab \times \left(-a^2b\right). \]

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Simplify the following expression:

\[ 16 x^3 \div \left( \frac{4}{3} x^2 \right). \]

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Simplify \[a^{-2} b^3 \times a^5 b^{-2} \div \left( a^2 b \right). \]

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Simplify \[ \frac{9 a^2 b \times 2 c}{36 a c^2} .\]

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