91Ó°ÊÓ

Perform the indicated operations, expressing answers in simplest form with rationalized denominators. $$(3+\sqrt{6-7 a})(2-\sqrt{6-7 a})$$

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

Write each expression in simplest radical form. If \(a\) radical appears in the denominator, rationalize the denominator. $$\sqrt[6]{b^{3} c^{4}}$$

Express each radical in simplest form, rationalize denominators, and perform the indicated operations. Then use a calculator to verify the result. $$2 \sqrt{40}+3 \sqrt{90}-5 \sqrt{250}$$

Express each radical in simplest form, rationalize denominators, and perform the indicated operations. Then use a calculator to verify the result. $$2 \sqrt{\frac{2}{3}}+\sqrt{24}-5 \sqrt{\frac{3}{2}}$$

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

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

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

Use a calculator to evaluate each expression. $$\frac{y^{3 / 8}\left(y^{5 / 8}-y^{13 / 8}\right)}{y^{1 / 2}\left(y^{1 / 2}-y^{-1 / 2}\right)}$$

Write each expression in simplest radical form. If \(a\) radical appears in the denominator, rationalize the denominator. $$\frac{\sqrt[4]{640}}{\sqrt[4]{5}}$$