91Ó°ÊÓ

Write each expression in simplest radical form. If \(a\) radical appears in the denominator, rationalize the denominator. $$\sqrt[5]{\sqrt[4]{9}}$$

Express each of the given expressions in simplest form with only positive exponents. $$2\left(3^{-3}-9^{-1}\right)^{-2}$$

Find the exact sum of the positive roots of \(x^{2}-2 x-2=0\) and \(x^{2}+2 x-11=0\).

Express each of the given expressions in simplest form with only positive exponents. $$\frac{6^{-1}}{4^{-2}+2}$$

Perform the indicated operations, expressing answers in simplest form with rationalized denominators. Then verify the result with a calculator. $$(\sqrt{11}+\sqrt{6})(\sqrt{11}-2 \sqrt{6})$$

Write each expression in simplest radical form. If \(a\) radical appears in the denominator, rationalize the denominator. $$\sqrt{\sqrt{\sqrt{n}}}$$

For the quadratic equation \(a x^{2}+b x+c=0,\) if \(a, b,\) and \(c\) are integers, the sum of the roots is a rational number. Explain.

Express each of the given expressions in simplest form with only positive exponents. $$\frac{x-y^{-1}}{x^{-1}-y}$$

Perform the indicated operations, expressing answers in simplest form with rationalized denominators. Then verify the result with a calculator. $$(2 \sqrt{5}-\sqrt{7})(3 \sqrt{5}+\sqrt{7})$$

Write each expression in simplest radical form. If \(a\) radical appears in the denominator, rationalize the denominator. $$\sqrt{b^{4} \sqrt{a}}$$