91Ó°ÊÓ

Perform the indicated operations, expressing answers in simplest form with rationalized denominators. $$\frac{\sqrt{15}-3 \sqrt{5}}{2 \sqrt{15}-\sqrt{5}}$$

Write each expression in simplest radical form. If a radical appears in the denominator, rationalize the denominator. $$\sqrt[9]{-27}$$

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

Simplify the given expressions. Express all answers with positive exponents. $$\frac{s^{1 / 4} s^{2 / 3}}{5 s^{-1}}$$

Perform the indicated operations, expressing answers in simplest form with rationalized denominators. $$\frac{6 \sqrt{x}}{\sqrt{x}-\sqrt{5}}$$

Write each expression in simplest radical form. If \(a\) radical appears in the denominator, rationalize the denominator. \(\sqrt{4 \times 10^{4}}\)

Simplify the given expressions. Express all answers with positive exponents. $$\frac{x^{3 / 10}}{x^{-1 / 5} x^{2}}$$

Express each of the given expressions in simplest form with only positive exponents. $$3 a^{-2}+\left(3 a^{-2}\right)^{4}$$

Express each radical in simplest form, rationalize denominators, and perform the indicated operations. $$\sqrt{\frac{T-V}{T+V}}-\sqrt{\frac{T+V}{T-V}}$$

In Exercises \(5-52,\) express each of the given expressions in simplest form with only positive exponents. $$3 a^{-2}+\left(3 a^{-2}\right)^{4}$$