91Ó°ÊÓ

Simplify the given expressions. Express all answers with positive exponents. $$x^{5 / 6} x^{-1 / 3}$$

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

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

Express each of the given expressions in simplest form with only positive exponents. $$5 \times 8^{-2}-3^{-1} \times 2^{3}$$

Express each radical in simplest form, rationalize denominators, and perform the indicated operations. Then use a calculator to verify the result. $$3 \sqrt{45}+3 \sqrt{75}-2 \sqrt{500}$$

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

Combine the terms into a single fraction, but do not rationalize the denominators. $$\frac{x^{2}}{\sqrt{2 x+1}}+2 x \sqrt{2 x+1}$$

Write each expression in simplest radical form. If \(a\) radical appears in the denominator, rationalize the denominator. \(\sqrt{\frac{5}{4}-\frac{1}{8}}\)

Write each expression in simplest radical form. If \(a\) radical appears in the denominator, rationalize the denominator. \(\sqrt{9 x^{2}-6 x+1}\)

Solve the given problems.Solve for \(x:\) $$x: \frac{1}{\left(2 x^{2}\right)^{-1}}=\frac{64}{x^{3}}$$.