91Ó°ÊÓ

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

Simplify each of the following. Express final results using positive exponents only. For example,\(\left(2 x^{\frac{1}{2}}\right)\left(3 x^{\frac{1}{3}}\right)=6 x^{\frac{5}{6}}\). \(\left(\frac{6 x^{\frac{2}{5}}}{7 y^{\frac{2}{3}}}\right)^{2}\)

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

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

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

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. For example,\(\left(2 x^{\frac{1}{2}}\right)\left(3 x^{\frac{1}{3}}\right)=6 x^{\frac{5}{6}}\). \(\left(\frac{2 x^{\frac{1}{3}}}{3 y^{\frac{1}{4}}}\right)^{4}\)

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

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

Simplify each of the following. Express final results using positive exponents only. For example,\(\left(2 x^{\frac{1}{2}}\right)\left(3 x^{\frac{1}{3}}\right)=6 x^{\frac{5}{6}}\). \(\left(\frac{x^{2}}{y^{3}}\right)^{-\frac{1}{2}}\)