91Ó°ÊÓ

Express each of the given expressions in simplest form with only positive exponents. $$6^{-2}\left(2 a-b^{-2}\right)^{-1}$$

Use a calculator to evaluate each expression. $$\frac{3^{-1} a^{1 / 2}}{4^{-1 / 2} b} \div \frac{9^{1 / 2} a^{-1 / 3}}{2 b^{-1 / 4}}$$

Express each radical in simplest form, rationalize denominators, and perform the indicated operations. Then use a calculator to verify the result. $$\sqrt{\frac{2}{7}}-2 \sqrt{\frac{7}{2}}+5 \sqrt{56}$$

Perform the indicated operations, expressing answers in simplest form with rationalized denominators. $$\frac{\sqrt{1+a}}{a-\sqrt{1-a}}$$

Perform the indicated operations, expressing answers in simplest form with rationalized denominators. $$\frac{\sqrt{a}+\sqrt{a-2}}{\sqrt{a}-\sqrt{a-2}}$$

Write each expression in simplest radical form. If \(a\) radical appears in the denominator, rationalize the denominator. $$\sqrt[4]{\sqrt[3]{16}}$$

Express each radical in simplest form, rationalize denominators, and perform the indicated operations. Then use a calculator to verify the result. $$2 \sqrt[3]{16}-\sqrt[3]{\frac{1}{4}}$$

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

Express each radical in simplest form, rationalize denominators, and perform the indicated operations. Then use a calculator to verify the result. $$5 \sqrt[4]{810}-\sqrt[4]{\frac{5}{8}}$$

Perform the indicated operations, expressing answers in simplest form with rationalized denominators. $$\frac{\sqrt{T^{4}-V^{4}}}{\sqrt{V^{-2}-T^{-2}}}$$