91Ó°ÊÓ

Simplify each expression. Assume that all variables in a radicand represent positive real numbers and no radicands involve negative quantities raised to even powers. $$-2 x^{2} y(\sqrt[3]{54 x^{3} y^{7} z^{2}})$$

In Exercises \(75-92,\) rationalize each denominator. Simplify, if possible. $$\frac{25}{5 \sqrt{2}-3 \sqrt{5}}$$

In Exercises \(79-112\), use rational exponents to simplify each expression. If rational exponents appear after simplifying. write the answer in radical notation. Assume that all variables represent positive numbers. $$\sqrt[5]{x^{10} y^{15}}$$

simplify each expression. Include absolute value bars where necessary. $$\sqrt[3]{(-5)^{3}}$$

Solve each equation. $$\sqrt{\sqrt{x}+\sqrt{x+9}}=3$$

Simplify each expression. Assume that all variables in a radicand represent positive real numbers and no radicands involve negative quantities raised to even powers. $$\frac{-x^{2} y^{7}}{2}(\sqrt[3]{-32 x^{4} y^{9} z^{7}})$$

Solve each equation. $$(x-4)^{\frac{2}{3}}=25$$

simplify each expression. Include absolute value bars where necessary. $$\sqrt[3]{(-6)^{3}}$$

In Exercises \(79-112\), use rational exponents to simplify each expression. If rational exponents appear after simplifying. write the answer in radical notation. Assume that all variables represent positive numbers. $$\sqrt[5]{x^{15} y^{20}}$$

In Exercises \(63-84,\) divide and simplify to the form \(a+b i\) $$\frac{5+i}{-4 i}$$