Chapter 10

Rationalize each denominator. Assume that all variables represent positive real numbers. \(\frac{2 \sqrt{a}-3}{2 \sqrt{a}-\sqrt{b}}\)

Write with positive exponents. Simplify if possible. $$ \frac{1}{n^{-8 / 9}} $$

Add or subtract as indicated. Assume that all variables represent positive real numbers. $$ \frac{\sqrt[4]{48}}{5 x}-\frac{2 \sqrt[4]{3}}{10 x} $$

Multiply. Write your answers in the form \(a+b i\). $$ 5 i(4-7 i) $$

Solve. $$ x-\sqrt{1-x}=-5 $$

Rationalize each denominator. Assume that all variables represent positive real numbers. \(\frac{8}{1+\sqrt{10}}\)

Write with positive exponents. Simplify if possible. $$ \frac{5}{7 x^{-3 / 4}} $$

Add or subtract as indicated. Assume that all variables represent positive real numbers. $$ \sqrt{\frac{28}{x^{2}}}+\sqrt{\frac{7}{4 x^{2}}} $$

Use the quotient rule to simplify. Assume that all variables represent positive real numbers. $$ \sqrt{100 x^{5}} $$

Multiply. Write your answers in the form \(a+b i\). $$ -3 i(-1+9 i) $$

Solve. $$ x-\sqrt{x-2}=4 $$

Rationalize each denominator. Assume that all variables represent positive real numbers. \(\frac{-3}{\sqrt{6}-2}\)

Find each root. Assume that all variables represent nonnegative real numbers. $$ \sqrt[5]{-1} $$

Write with positive exponents. Simplify if possible. $$ \frac{2}{3 y^{-5 / 7}} $$

Add or subtract as indicated. Assume that all variables represent positive real numbers. $$ \frac{\sqrt{99}}{5 x}-\sqrt{\frac{44}{x^{2}}} $$

Use the quotient rule to simplify. Assume that all variables represent positive real numbers. $$ \sqrt{64 y^{9}} $$

Multiply. Write your answers in the form \(a+b i\). $$ -5 i(-2+i) $$

Solve. $$ \sqrt[3]{-6 x-1}=\sqrt[3]{-2 x-5} $$

Rationalize each denominator. Assume that all variables represent positive real numbers. \(\frac{\sqrt{x}}{\sqrt{x}+\sqrt{y}}\)

Find each root. Assume that all variables represent nonnegative real numbers. $$ \sqrt[5]{x^{20}} $$

Use the properties of exponents to simplify each expression. Write with positive exponents. $$ a^{2 / 3} a^{5 / 3} $$

Add or subtract as indicated. Assume that all variables represent positive real numbers. $$ \sqrt[3]{\frac{16}{27}}-\frac{\sqrt[3]{54}}{6} $$

Use the quotient rule to simplify. Assume that all variables represent positive real numbers. $$ \sqrt[3]{16 y^{7}} $$

Multiply. Write your answers in the form \(a+b i\). $$ (4+i)(5+2 i) $$

Solve. $$ x+\sqrt{x+5}=7 $$

Rationalize each denominator. Assume that all variables represent positive real numbers. \(\frac{2 \sqrt{a}}{2 \sqrt{x}-\sqrt{y}}\)

Find each root. Assume that all variables represent nonnegative real numbers. $$ \sqrt[4]{x^{20}} $$

Use the properties of exponents to simplify each expression. Write with positive exponents. $$ b^{9 / 5} b^{8 / 5} $$

Add or subtract as indicated. Assume that all variables represent positive real numbers. $$ \frac{\sqrt[3]{3}}{10}+\sqrt[3]{\frac{24}{125}} $$

Use the quotient rule to simplify. Assume that all variables represent positive real numbers. $$ \sqrt[3]{128 y^{10}} $$

Multiply. Write your answers in the form \(a+b i\). $$ (3+i)(2+4 i) $$

Solve. $$ \sqrt{5 x-1}-\sqrt{x}+2=3 $$

Rationalize each denominator. Assume that all variables represent positive real numbers. \(\frac{2 \sqrt{3}+\sqrt{6}}{4 \sqrt{3}-\sqrt{6}}\)

Find each root. Assume that all variables represent nonnegative real numbers. $$ \sqrt[6]{64 x^{12}} $$

Use the properties of exponents to simplify each expression. Write with positive exponents. $$ x^{-2 / 5} \cdot x^{7 / 5} $$

Add or subtract as indicated. Assume that all variables represent positive real numbers. $$ \frac{\sqrt[3]{2 x^{4}}}{9}+\sqrt[3]{\frac{250 x^{4}}{27}} $$

Use the quotient rule to simplify. Assume that all variables represent positive real numbers. $$ \sqrt[4]{a^{8} b^{7}} $$

Multiply. Write your answers in the form \(a+b i\). $$ (\sqrt{3}+2 i)(\sqrt{3}-2 i) $$

Solve. $$ \sqrt{2 x-1}-4=-\sqrt{x-4} $$

Rationalize each denominator. Assume that all variables represent positive real numbers. \(\frac{4 \sqrt{5}+\sqrt{2}}{2 \sqrt{5}-\sqrt{2}}\)

Use the properties of exponents to simplify each expression. Write with positive exponents. $$ y^{4 / 3} \cdot y^{-1 / 3} $$

Add or subtract as indicated. Assume that all variables represent positive real numbers. $$ \frac{\sqrt[3]{y^{5}}}{8}+\frac{5 y \sqrt[3]{y^{2}}}{4} $$

Use the quotient rule to simplify. Assume that all variables represent positive real numbers. $$ \sqrt[5]{32 z^{12}} $$

Multiply. Write your answers in the form \(a+b i\). $$ (\sqrt{5}-5 i)(\sqrt{5}+5 i) $$

Rationalize each numerator. Assume that all variables represent positive real numbers. \(\sqrt{\frac{5}{3}}\)

Solve. $$ \sqrt{2 x-1}=\sqrt{1-2 x} $$

Find each root. Assume that all variables represent nonnegative real numbers. $$ \sqrt{81 x^{4}} $$

Use the properties of exponents to simplify each expression. Write with positive exponents. $$ 3^{1 / 4} \cdot 3^{3 / 8} $$

Multiply. Write your answers in the form \(a+b i\). $$ (4-2 i)^{2} $$

Rationalize each numerator. Assume that all variables represent positive real numbers. \(\sqrt{\frac{3}{2}}\)