91Ó°ÊÓ

Explain how to add like radicals. Give an example with your explanation.

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. $$\sqrt[12]{(3 y)^{2}}$$

In Exercises \(85-100,\) simplify each expression. $$i^{15}$$

Simplify each expression. Assume that all variables in a radicand represent positive real numbers and no radicands involve negative quantities raised to even powers. $$\left(-5 x^{2} y^{3} z \sqrt{2 x y z}\right)\left(-x^{4} z \sqrt{10 x z}\right)$$

simplify each expression. Include absolute value bars where necessary. $$\sqrt[4]{(x+5)^{4}}$$

Exercises \(88-90\) will help you prepare for the material covered in the next section. Simplify: \((-5+7 x)-(-11-6 x)\)

Simplify each expression. Assume that all variables in a radicand represent positive real numbers and no radicands involve negative quantities raised to even powers. $$\left(2 x^{2} y \sqrt[4]{8 x y}\right)\left(-3 x y^{2} \sqrt[4]{2 x^{2} y^{3}}\right)$$

simplify each expression. Include absolute value bars where necessary. $$\sqrt[5]{-32(x-1)^{5}}$$

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

In Exercises \(85-100,\) simplify each expression. $$i^{22}$$