Algebra
Polynomial Arithmetic
Simplify \[\frac{1}{2} ab \times \left(-a^2b\right). \]
Simplify the following expression:
\[ 16 x^3 \div \left( \frac{4}{3} x^2 \right). \]
Simplify \[a^{-2} b^3 \times a^5 b^{-2} \div \left( a^2 b \right). \]
A rectangular cuboid with its base measuring \(4ab^2 \text{ cm}\) by \(3a^2 \text{ cm}\) has a volume of \( 36a^5b^6 \text{ cm}^3\). What is its height in \(\text{cm}\)?
Simplify \[ \frac{9 a^2 b \times 2 c}{36 a c^2} .\]