Chapter 5

Express each of the following in simplest radical form. All variables represent positive real numbers. \(\frac{\sqrt{5 y}}{\sqrt{18 x^{3}}}\)

Change each radical to simplest radical form. \(\sqrt{\frac{24}{49}}\)

Simplify each expression. Express final results without using zero or negative integers as exponents. \(x^{-3} \cdot x^{-4}\)

Use scientific notation and the properties of exponents to help you perform the following operations. \(\sqrt{9,000,000}\)

For Problems \(45-58\), write each of the following using positive rational exponents. For example, \(\sqrt{a b}=(a b)^{\frac{1}{2}}=a^{\frac{1}{2}} b^{\frac{1}{2}}\) \(\sqrt{5 y}\)

Solve each equation. Don't forget to check each of your potential solutions. \(\sqrt[3]{2 x+3}=-3\)

Find the following products and express answers in simplest radical form. All variables represent nonnegative real numbers. \((\sqrt{2}+\sqrt{10})(\sqrt{2}-\sqrt{10})\)

Express each of the following in simplest radical form. All variables represent positive real numbers. \(\frac{\sqrt{18 y^{3}}}{\sqrt{16 x}}\)

Change each radical to simplest radical form. \(\sqrt{\frac{2}{7}}\)

Simplify each expression. Express final results without using zero or negative integers as exponents. \(a^{3} \cdot a^{-5} \cdot a^{-1}\)

Use scientific notation and the properties of exponents to help you perform the following operations. \(\sqrt{0.00000009}\)

Write each of the following using positive rational exponents. For example, \(\sqrt{a b}=(a b)^{\frac{1}{2}}=a^{\frac{1}{2}} b^{\frac{1}{2}}\). \(\sqrt{2 x y}\)

Solve each equation. Don't forget to check each of your potential solutions. \(\sqrt[3]{3 x-1}=-4\)

Find the following products and express answers in simplest radical form. All variables represent nonnegative real numbers. \((2 \sqrt{3}+\sqrt{11})(2 \sqrt{3}-\sqrt{11})\)

Express each of the following in simplest radical form. All variables represent positive real numbers. \(\frac{\sqrt{2 x^{3}}}{\sqrt{9 y}}\)

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

Simplify each expression. Express final results without using zero or negative integers as exponents. \(b^{-2} \cdot b^{3} \cdot b^{-6}\)

Use scientific notation and the properties of exponents to help you perform the following operations. \(\sqrt[3]{8000}\)

Write each of the following using positive rational exponents. For example, \(\sqrt{a b}=(a b)^{\frac{1}{2}}=a^{\frac{1}{2}} b^{\frac{1}{2}}\). \(3 \sqrt{y}\)

Solve each equation. Don't forget to check each of your potential solutions. \(\sqrt[3]{2 x+5}=\sqrt[3]{4-x}\)

Find the following products and express answers in simplest radical form. All variables represent nonnegative real numbers. \((\sqrt{2 x}+\sqrt{3 y})(\sqrt{2 x}-\sqrt{3 y})\)

Express each of the following in simplest radical form. All variables represent positive real numbers. \(\frac{\sqrt{24 a^{2} b^{3}}}{\sqrt{7 a b^{6}}}\)

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

Simplify each expression. Express final results without using zero or negative integers as exponents. \(\left(a^{-4}\right)^{2}\)

Use scientific notation and the properties of exponents to help you perform the following operations. \(\sqrt[3]{0.001}\)

Write each of the following using positive rational exponents. For example, \(\sqrt{a b}=(a b)^{\frac{1}{2}}=a^{\frac{1}{2}} b^{\frac{1}{2}}\). \(5 \sqrt{a b}\)

Solve each equation. Don't forget to check each of your potential solutions. \(\sqrt[3]{3 x-1}=\sqrt[3]{2-5 x}\)

Find the following products and express answers in simplest radical form. All variables represent nonnegative real numbers. \((2 \sqrt{x}-5 \sqrt{y})(2 \sqrt{x}+5 \sqrt{y})\)

Express each of the following in simplest radical form. All variables represent positive real numbers. \(\frac{\sqrt{12 a^{2} b}}{\sqrt{5 a^{3} b^{3}}}\)

Change each radical to simplest radical form. \(\sqrt{\frac{7}{12}}\)

Simplify each expression. Express final results without using zero or negative integers as exponents. \(\left(b^{4}\right)^{-3}\)

Use scientific notation and the properties of exponents to help you perform the following operations. \((90,000)^{\frac{3}{2}}\)

Write each of the following using positive rational exponents. For example, \(\sqrt{a b}=(a b)^{\frac{1}{2}}=a^{\frac{1}{2}} b^{\frac{1}{2}}\). \(\sqrt[3]{x y^{2}}\)

Solve each equation. Don't forget to check each of your potential solutions. \(\sqrt{x+19}-\sqrt{x+28}=-1\)

Find the following products and express answers in simplest radical form. All variables represent nonnegative real numbers. \(2 \sqrt[3]{3}(5 \sqrt[3]{4}+\sqrt[3]{6})\)

Express each of the following in simplest radical form. All variables represent positive real numbers. \(\sqrt[3]{24 y}\)

Change each radical to simplest radical form. \(\frac{\sqrt{5}}{\sqrt{12}}\)

Simplify each expression. Express final results without using zero or negative integers as exponents. \(\left(x^{2} y^{-6}\right)^{-1}\)

Use scientific notation and the properties of exponents to help you perform the following operations. \((8000)^{\frac{2}{3}}\)

Write each of the following using positive rational exponents. For example, \(\sqrt{a b}=(a b)^{\frac{1}{2}}=a^{\frac{1}{2}} b^{\frac{1}{2}}\). \(\sqrt[5]{x^{2} y^{4}}\)

Solve each equation. Don't forget to check each of your potential solutions. \(\sqrt{x+4}=\sqrt{x-1}+1\)

Find the following products and express answers in simplest radical form. All variables represent nonnegative real numbers. \(2 \sqrt[3]{2}(3 \sqrt[3]{6}-4 \sqrt[3]{5})\)

Express each of the following in simplest radical form. All variables represent positive real numbers. \(\sqrt[3]{16 x^{2}}\)

Change each radical to simplest radical form. \(\frac{\sqrt{3}}{\sqrt{7}}\)

Simplify each expression. Express final results without using zero or negative integers as exponents. \(\left(x^{5} y^{-1}\right)^{-3}\)

Avogadro's number, \(602,000,000,000,000,000,000,000\), is the number of atoms in 1 mole of a substance. Express this number in scientific notation.

Write each of the following using positive rational exponents. For example, \(\sqrt{a b}=(a b)^{\frac{1}{2}}=a^{\frac{1}{2}} b^{\frac{1}{2}}\). \(\sqrt[4]{a^{2} b^{3}}\)

Solve each equation. Don't forget to check each of your potential solutions. \(\sqrt{3 x+1}+\sqrt{2 x+4}=3\)

Find the following products and express answers in simplest radical form. All variables represent nonnegative real numbers. \(3 \sqrt[3]{4}(2 \sqrt[3]{2}-6 \sqrt[3]{4})\)

Express each of the following in simplest radical form. All variables represent positive real numbers. \(\sqrt[3]{16 x^{4}}\)