Chapter 7: Chapter 7

Find the product $4 \sqrt{\left(x^{3} y\right)} \cdot{ }^{4} \sqrt{\left(x y^{2}\right)}$ and simplify.

Simplify ${ }^{3} \sqrt{\left(-81 x^{3}\right)}-2 x^{3} \sqrt{3}+5 x^{3} \sqrt{24}$

Write in radical form without negative exponents, rationalizing denominators: (a) \(\left(\mathrm{x}^{1 / 3}\right)^{-3 / 4}\) (b) \(x^{1 / 6} / x^{-2 / 3}\)

Rationalize \(\quad 3 \sqrt{3 a x} /{ }^{3} \sqrt{4 a^{2}}\)

Express the product $\left(1 /{ }^{3} \sqrt{\mathrm{x}}^{2}\right) \cdot\left(1 /{ }^{4} \sqrt{\mathrm{x}}\right)$ in simplest radical form, rationalizing the denominator.

Rationalize the denominator in the quotient: \(1 /(\sqrt{x}-\sqrt{y})\)

Reduce \((2+3 \sqrt{-1})^{2} /(2+\sqrt{-1})\) to the form $\mathrm{A}+\mathrm{B} \sqrt{-1}$.

Express with rational denominator $4 /\left({ }^{3} \sqrt{9}-{ }^{3} \sqrt{3}+1\right)$.

Find the product $\left.{ }^{3} \sqrt{(} 2 \mathrm{a}^{2} \mathrm{x}\right) \cdot \sqrt{(2 \mathrm{x})}$

Simplify \(\quad(\sqrt{3}+\sqrt{2}) \cdot(\sqrt{2}-\sqrt{6})\)