91Ó°ÊÓ

Simplify each of the following. Express final results using positive exponents only. For example,\(\left(2 x^{\frac{1}{2}}\right)\left(3 x^{\frac{1}{3}}\right)=6 x^{\frac{5}{6}}\). \(\frac{48 b^{\frac{1}{3}}}{12 b^{\frac{3}{4}}}\)

Use the distributive property to help simplify each of the following. All variables represent positive real numbers. \(7 \sqrt{4 a b}-\sqrt{16 a b}-10 \sqrt{25 a b}\)

Find the indicated products and quotients. Express final results using positive integral exponents only. \(\left(\frac{35 x^{-1} y^{-2}}{7 x^{4} y^{3}}\right)^{-1}\)

Rationalize the denominator and simplify. All variables represent positive real numbers. \(\frac{\sqrt{x}-2}{\sqrt{x}+6}\)

Use the distributive property to help simplify each of the following. All variables represent positive real numbers. \(4 \sqrt{a b}-9 \sqrt{36 a b}+6 \sqrt{49 a b}\)

Change each radical to simplest radical form. \(\frac{\sqrt[3]{8}}{\sqrt[3]{16}}\)

Simplify each of the following. Express final results using positive exponents only. For example,\(\left(2 x^{\frac{1}{2}}\right)\left(3 x^{\frac{1}{3}}\right)=6 x^{\frac{5}{6}}\). \(\frac{56 a^{\frac{1}{6}}}{8 a^{\frac{1}{4}}}\)

Find the indicated products and quotients. Express final results using positive integral exponents only. \(\left(\frac{-48 a b^{2}}{-6 a^{3} b^{5}}\right)^{-2}\)

Rationalize the denominator and simplify. All variables represent positive real numbers. \(\frac{\sqrt{x}+1}{\sqrt{x}-10}\)

Use the distributive property to help simplify each of the following. All variables represent positive real numbers. \(-3 \sqrt{2 x^{3}}+4 \sqrt{8 x^{3}}-3 \sqrt{32 x^{3}}\)