91Ó°ÊÓ

Find the indicated products and quotients. Express final results using positive integral exponents only. \(\left(\frac{-36 a^{-1} b^{-6}}{4 a^{-1} b^{4}}\right)^{-2}\)

Simplify each of the following. Express final results using positive exponents only. $$ \left(\frac{6 x^{\frac{2}{5}}}{7 y^{\frac{2}{3}}}\right)^{2} $$

Rationalize the denominator and simplify. All variables represent positive real numbers. $$ \frac{\sqrt{x}}{\sqrt{x}+2 \sqrt{y}} $$

Change each radical to simplest radical form. \(\frac{\sqrt[3]{6}}{\sqrt[3]{4}}\)

For Problems \(65-74\), use the distributive property to help simplify each of the following. All variables represent positive real numbers. $$ -3 \sqrt{2 x^{3}}+4 \sqrt{8 x^{3}}-3 \sqrt{32 x^{3}} $$

Change each radical to simplest radical form. \(\frac{\sqrt[3]{4}}{\sqrt[3]{2}}\)

Find the indicated products and quotients. Express final results using positive integral exponents only. \(\left(\frac{8 x y^{3}}{-4 x^{4} y}\right)^{-3}\)

Rationalize the denominator and simplify. All variables represent positive real numbers. $$ \frac{\sqrt{y}}{2 \sqrt{x}-\sqrt{y}} $$

For Problems \(65-74\), use the distributive property to help simplify each of the following. All variables represent positive real numbers. $$ 2 \sqrt{40 x^{5}}-3 \sqrt{90 x^{5}}+5 \sqrt{160 x^{5}} $$

Simplify each of the following. Express final results using positive exponents only. $$ \left(\frac{2 x^{\frac{1}{3}}}{3 y^{\frac{1}{4}}}\right)^{4} $$