91Ó°ÊÓ

In Exercises \(5-52,\) express each of the given expressions in simplest form with only positive exponents. $$2 \times 3^{-1}+4 \times 3^{-2}$$

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

In Exercises \(5-52,\) express each of the given expressions in simplest form with only positive exponents. $$5 \times 8^{-2}-3^{-1} \times 2^{3}$$

Simplify the given expressions. Express all answers with positive exponents. $$\left(8 b^{-4} c^{2}\right)^{4 / 3}$$

Perform the indicated operations, expressing answers in simplest form with rationalized denominators. $$\sqrt[3]{5-\sqrt{17}} \sqrt[3]{5+\sqrt{17}}$$

Write each expression in simplest radical form. If \(a\) radical appears in the denominator, rationalize the denominator. \(\sqrt[3]{16 \times 10^{5}}\)

Express each radical in simplest form, rationalize denominators, and perform the indicated operations. $$3 \sqrt{50 y-75}-\sqrt{8 y-12}$$

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

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

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