Chapter 7

$$ (4-7 i)+(2+3 i) $$

Use radical notation to write each expression. Simplify if possible. $$ \left(\frac{16}{9}\right)^{3 / 2} $$

Solve. \(\sqrt{3 x+1}+2=0\)

Add or subtract. $$ 5 y \sqrt{8 y}+2 \sqrt{50 y^{3}} $$

Find each cube root. $$ \sqrt[3]{-64 x^{6}} $$

Add or subtract. Write the sum or difference in the form \(a+b i .\) See Example 3 $$ (2-4 i)-(2-i) $$

Use radical notation to write each expression. Simplify if possible. $$ \left(\frac{49}{25}\right)^{3 / 2} $$

Solve. \(\sqrt{3 x+1}-2=0\)

Add or subtract. $$ 3 \sqrt{8 x^{2} y^{3}}-2 x \sqrt{32 y^{3}} $$

Find each root. Assume that all variables represent nonnegative real numbers. $$ -\sqrt[4]{16} $$

Write with positive exponents. Simplify if possible. $$ 8^{-4 \sqrt{3}} $$

Add or subtract. Write the sum or difference in the form \(a+b i .\) See Example 3 $$ (6+5 i)-(8-i) $$

Solve. \(\sqrt[4]{4 x+1}-2=0\)

Add or subtract. $$ \sqrt[3]{54 x y^{3}}-5 \sqrt[3]{2 x y^{3}}+y \sqrt[3]{128 x} $$

Rationalize each denominator. See Examples 1 through 3. $$ \sqrt[4]{\frac{81}{8}} $$

Write with positive exponents. Simplify if possible. $$ 64^{-2 / 3} $$

Add or subtract. Write the sum or difference in the form \(a+b i .\) See Example 3 $$ (8-3 i)+(-8+3 i) $$

Solve. \(\sqrt[4]{2 x-9}-3=0\)

Add or subtract. $$ 2 \sqrt[3]{24 x^{3} y^{4}}+4 x \sqrt[3]{81 y^{4}} $$

Find each root. Assume that all variables represent nonnegative real numbers. $$ \sqrt[5]{-243} $$

Rationalize each denominator. See Examples 1 through 3. $$ \sqrt[4]{\frac{1}{9}} $$

Write with positive exponents. Simplify if possible. $$ (-64)^{-2 / 3} $$

Add or subtract. Write the sum or difference in the form \(a+b i .\) See Example 3 $$ 6-(8+4 i) $$

Solve. \(\sqrt{4 x-3}=7\)

Simplify. See Examples 3 and 4 $$ \sqrt{32} $$

Add or subtract. $$ 6 \sqrt[3]{11}+8 \sqrt{11}-12 \sqrt{11} $$

Rationalize each denominator. See Examples 1 through 3. $$ \sqrt[4]{\frac{16}{9 x^{7}}} $$

Write with positive exponents. Simplify if possible. $$ (-8)^{-4 / 3} $$

Add or subtract. Write the sum or difference in the form \(a+b i .\) See Example 3 $$ (9-4 i)-9 $$

Solve. \(\sqrt{3 x+9}=6\)

Rationalize each denominator. See Examples 1 through 3. $$ \sqrt[5]{\frac{32}{m^{6} n^{13}}} $$

Add or subtract. $$ 3 \sqrt[3]{5}+4 \sqrt{5}-8 \sqrt{5} $$

Simplify. See Examples 3 and 4 $$ \sqrt{27} $$

Multiply. Write the product in the form \(a+b i .\) See Example 4. $$ -10 i \cdot-4 i $$

Write with positive exponents. Simplify if possible. $$ (-4)^{-3 / 2} $$

Solve. \(\sqrt[3]{6 x-3}-3=0\)

Add or subtract. $$ -2 \sqrt[4]{x^{7}}+3 \sqrt[4]{16 x^{7}}-x \sqrt[4]{x^{3}} $$

Multiply. Write the product in the form \(a+b i .\) See Example 4. $$ -2 i \cdot-11 i $$

Write with positive exponents. Simplify if possible. $$ (-16)^{-5 / 4} $$

Solve. \(\sqrt[3]{3 x}+4=7\)

Rationalize each denominator. See Examples 1 through 3. $$ \frac{9 y}{\sqrt[4]{4 y^{9}}} $$

Simplify. See Examples 3 and 4 $$ \sqrt[3]{108} $$

Add or subtract. $$ 6 \sqrt[3]{24 x^{3}}-2 \sqrt[3]{81 x^{3}}-x \sqrt[3]{3} $$

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

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

Multiply. Write the product in the form \(a+b i .\) See Example 4. $$ 6 i(2-3 i) $$

Write with positive exponents. Simplify if possible. $$ x^{-1 / 4} $$

Solve. \(\sqrt[3]{2 x-3}-2=-5\)

Write the conjugate of each expression. $$ \sqrt{2}+x $$

Simplify. See Examples 3 and 4 $$ 5 \sqrt{75} $$