91Ó°ÊÓ

In Exercises \(5-52,\) express each of the given expressions in simplest form with only positive exponents. $$\left(2 n p^{-2}\right)^{-2}\left(4^{-1} p^{2}\right)^{-1}$$

Write each expression in simplest radical form. If a radical appears in the denominator, rationalize the denominator. $$\sqrt[8]{81}$$

Perform the indicated operations, expressing answers in simplest form with rationalized denominators. $$\frac{2 \sqrt{3}-5 \sqrt{5}}{\sqrt{3}+2 \sqrt{5}}$$

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

Write each expression in simplest radical form. If a radical appears in the denominator, rationalize the denominator. $$\sqrt[6]{64}$$

Express each radical in simplest form, rationalize denominators, and perform the indicated operations. $$\sqrt[3]{a b^{-1}}-\sqrt[3]{8 a^{-2} b^{2}}$$

Simplify the given expressions. Express all answers with positive exponents. $$\frac{4 y^{-1} 12}{-y^{2} y^{5}}$$

In Exercises \(5-52,\) express each of the given expressions in simplest form with only positive exponents. $$\left(\frac{V^{-1}}{2 t}\right)^{-2}\left(\frac{t^{2}}{V^{-2}}\right)^{-3}$$

In Exercises \(5-52,\) express each of the given expressions in simplest form with only positive exponents. $$a b\left(\frac{a^{-2}}{b^{2}}\right)^{-3}\left(\frac{a^{-3}}{b^{5}}\right)^{2}$$

Express each radical in simplest form, rationalize denominators, and perform the indicated operations. $$\sqrt{\frac{2 x y^{-1}}{3}}+\sqrt{\frac{27 x^{-1} y}{8}}$$