Chapter 5

Evaluate each numerical expression. \(\left(\frac{1}{8}\right)^{-\frac{2}{3}}\)

Solve each equation. Don't forget to check each of your potential solutions. \(\sqrt{3 x-2}-\sqrt{x+4}=0\)

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

Express each of the following in simplest radical form. All variables represent positive real numbers. \(\sqrt{75 x^{2}}\)

Change each radical to simplest radical form. \(\sqrt{32}\)

Simplify each numerical expression. \(\left(5^{3}\right)^{-1}\)

For Problems \(19-32\), write each of the following in ordinary decimal notation. For example, \((3.18)(10)^{2}=318\). \((7)(10)^{9}\)

Evaluate each numerical expression. \(\left(-\frac{1}{27}\right)^{-\frac{2}{3}}\)

Solve each equation. Don't forget to check each of your potential solutions. \(\sqrt{7 x-6}-\sqrt{5 x+2}=0\)

Find the following products and express answers in simplest radical form. All variables represent nonnegative real numbers. \(\sqrt{2 x}(3 \sqrt{y}-7 \sqrt{5})\)

Express each of the following in simplest radical form. All variables represent positive real numbers. \(\sqrt{108 y^{2}}\)

Change each radical to simplest radical form. \(\sqrt{98}\)

Simplify each numerical expression. \(\left(3^{-1}\right)^{3}\)

For Problems \(19-32\), write each of the following in ordinary decimal notation. For example, \((3.18)(10)^{2}=318\). \((3.14)(10)^{10}\)

Evaluate each numerical expression. \(64^{-\frac{7}{6}}\)

Solve each equation. Don't forget to check each of your potential solutions. \(5 \sqrt{t-1}=6\)

Find the following products and express answers in simplest radical form. All variables represent nonnegative real numbers. \(\sqrt{x y}(5 \sqrt{x y}-6 \sqrt{x})\)

Express each of the following in simplest radical form. All variables represent positive real numbers. \(\sqrt{20 x^{2} y}\)

Change each radical to simplest radical form. \(\sqrt{80}\)

Simplify each numerical expression. \(\left(2^{3} \cdot 3^{-2}\right)^{-1}\)

For Problems \(19-32\), write each of the following in ordinary decimal notation. For example, \((3.18)(10)^{2}=318\). \((2.04)(10)^{12}\)

Evaluate each numerical expression. \(32^{-\frac{4}{5}}\)

Solve each equation. Don't forget to check each of your potential solutions. \(4 \sqrt{t+3}=6\)

Find the following products and express answers in simplest radical form. All variables represent nonnegative real numbers. \(4 \sqrt{x}(2 \sqrt{x y}+2 \sqrt{x})\)

Express each of the following in simplest radical form. All variables represent positive real numbers. \(\sqrt{80 x y^{2}}\)

Change each radical to simplest radical form. \(\sqrt{125}\)

Simplify each numerical expression. \(\left(2^{-2} \cdot 3^{-1}\right)^{-3}\)

For Problems \(19-32\), write each of the following in ordinary decimal notation. For example, \((3.18)(10)^{2}=318\). \((4.3)(10)^{-1}\)

Evaluate each numerical expression. \(-25^{\frac{3}{2}}\)

Solve each equation. Don't forget to check each of your potential solutions. \(\sqrt{x^{2}+7}=4\)

Find the following products and express answers in simplest radical form. All variables represent nonnegative real numbers. \(\sqrt{5 y}\left(\sqrt{8 x}+\sqrt{12 y^{2}}\right)\)

Express each of the following in simplest radical form. All variables represent positive real numbers. \(\sqrt{64 x^{3} y^{7}}\)

Change each radical to simplest radical form. \(\sqrt{160}\)

Simplify each numerical expression. \(\left(4^{2} \cdot 5^{-1}\right)^{2}\)

Write each of the following in ordinary decimal notation. For example, \((3.18)(10)^{2}=318\). \((5.2)(10)^{-2}\)

Evaluate each numerical expression. \(-16^{\frac{3}{4}}\)

Solve each equation. Don't forget to check each of your potential solutions. \(\sqrt{x^{2}+3}-2=0\)

Find the following products and express answers in simplest radical form. All variables represent nonnegative real numbers. \(\sqrt{2 x}(\sqrt{12 x y}-\sqrt{8 y})\)

Express each of the following in simplest radical form. All variables represent positive real numbers. \(\sqrt{36 x^{5} y^{6}}\)

Change each radical to simplest radical form. \(\sqrt{112}\)

Simplify each numerical expression. \(\left(2^{-3} \cdot 4^{-1}\right)^{-1}\)

Write each of the following in ordinary decimal notation. For example, \((3.18)(10)^{2}=318\). \((9.14)(10)^{-4}\)

Evaluate each numerical expression. \(125^{\frac{4}{3}}\)

Solve each equation. Don't forget to check each of your potential solutions. \(\sqrt{x^{2}+13 x+37}=1\)

Find the following products and express answers in simplest radical form. All variables represent nonnegative real numbers. \(5 \sqrt{3}(2 \sqrt{8}-3 \sqrt{18})\)

Express each of the following in simplest radical form. All variables represent positive real numbers. \(\sqrt{54 a^{4} b^{3}}\)

Change each radical to simplest radical form. \(4 \sqrt{18}\)

Simplify each numerical expression. \(\left(\frac{2^{-1}}{5^{-2}}\right)^{-1}\)

Write each of the following in ordinary decimal notation. For example, \((3.18)(10)^{2}=318\). \((8.76)(10)^{-5}\)

Evaluate each numerical expression. \(81^{\frac{5}{4}}\)