91Ó°ÊÓ

If only like radicals can be combined, why is it possible to add \(\sqrt{2}\) and \(\sqrt{8} ?\)

Will help you prepare for the material covered in the next section. Multiply: \(\quad(7-3 x)(-2-5 x)\)

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. $$(\sqrt[6]{2 a})^{4}$$

Simplify each expression. Assume that all variables in a radicand represent positive real numbers and no radicands involve negative quantities raised to even powers. $$\left(5 a^{2} b \sqrt[4]{8 a^{2} b}\right)(4 a b \sqrt[4]{4 a^{3} b^{2}})$$

In Exercises \(75-92,\) rationalize each denominator. Simplify, if possible. $$\frac{2 \sqrt{6}+\sqrt{5}}{3 \sqrt{6}-\sqrt{5}}$$

In Exercises \(85-100,\) simplify each expression. $$i^{46}$$

Explain how to simplify a radical expression using the quotient rule. Provide an example.

Will help you prepare for the material covered in the next section. Rationalize the denominator: \(\frac{7+4 \sqrt{2}}{2-5 \sqrt{2}}\)

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. $$(\sqrt[6]{2 a})^{6}$$

simplify each expression. Include absolute value bars where necessary. $$\sqrt[5]{-32(x-2)^{5}}$$