Chapter 10

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

Rationalize each denominator. Assume that all variables represent positive real numbers. \(\frac{9 y}{\sqrt[4]{4 y^{9}}}\)

Find each cube root. $$ \sqrt{-125} $$

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

Add or subtract as indicated. Assume that all variables represent positive real numbers. $$ 2 \sqrt[3]{24 x^{3} y^{4}}+4 x \sqrt[3]{81 y^{4}} $$

Use the quotient rule to simplify. Assume that all variables represent positive real numbers. $$ -\sqrt[3]{\frac{1000 a}{b^{9}}} $$

Add or subtract as indicated. Write your answers in the form \(a+b i .\) $$ (5-3 i)+(7-8 i) $$

Solve. $$ \sqrt{3 x+4}=5 $$

Rationalize each denominator. Assume that all variables represent positive real numbers. \(\frac{6}{2-\sqrt{7}}\)

Find each cube root. $$ \sqrt[3]{x^{12}} $$

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

Add or subtract as indicated. Assume that all variables represent positive real numbers. $$ 6 \sqrt[3]{11}+8 \sqrt{11}-12 \sqrt{11} $$

Simplify. Assume that all variables represent positive real numbers. $$ \sqrt{32} $$

Multiply. Write your answers in the form \(a+b i\). $$ 6 i \cdot 2 i $$

Solve. $$ \sqrt{3 x+9}=12 $$

Rationalize each denominator. Assume that all variables represent positive real numbers. \(\frac{3}{\sqrt{7}-4}\)

Find each cube root. $$ \sqrt[3]{x^{15}} $$

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

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

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

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

Rationalize each denominator. Assume that all variables represent positive real numbers. \(\frac{-7}{\sqrt{x}-3}\)

Find each cube root. $$ \sqrt[3]{-27 x^{9}} $$

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

Add or subtract as indicated. Assume that all variables represent positive real numbers. $$ -2 \sqrt[4]{x^{7}}+3 \sqrt[4]{16 x^{7}} $$

Multiply. Write your answers in the form \(a+b i\). $$ -9 i \cdot 7 i $$

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

Rationalize each denominator. Assume that all variables represent positive real numbers. \(\frac{-8}{\sqrt{y}+4}\)

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

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

Add or subtract as indicated. Assume that all variables represent positive real numbers. $$ 6 \sqrt[3]{24 x^{3}}-2 \sqrt[3]{81 x^{3}}-x \sqrt[3]{3} $$

Multiply. Write your answers in the form \(a+b i\). $$ -6 i \cdot 4 i $$

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

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

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

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

Add or subtract as indicated. Assume that all variables represent positive real numbers. $$ \frac{4 \sqrt{3}}{3}-\frac{\sqrt{12}}{3} $$

Multiply. Write your answers in the form \(a+b i\). $$ -10 i \cdot-4 i $$

Solve. $$ \sqrt[3]{x-4}-5=-7 $$

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

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

Write with positive exponents. Simplify if possible. $$ y^{-1 / 6} $$

Add or subtract as indicated. Assume that all variables represent positive real numbers. $$ \frac{\sqrt{45}}{10}+\frac{7 \sqrt{5}}{10} $$

Multiply. Write your answers in the form \(a+b i\). $$ -2 i \cdot-11 i $$

Solve. $$ \sqrt{x+4}=\sqrt{2 x-5} $$

Rationalize each denominator. Assume that all variables represent positive real numbers. \(\frac{\sqrt{a}+1}{2 \sqrt{a}-\sqrt{b}}\)

Write with positive exponents. Simplify if possible. $$ \frac{1}{a^{-2 / 3}} $$

Add or subtract as indicated. Assume that all variables represent positive real numbers. $$ \frac{\sqrt[3]{8 x^{4}}}{7}+\frac{3 x \sqrt[3]{x}}{7} $$

Multiply. Write your answers in the form \(a+b i\). $$ 6 i(2-3 i) $$

Solve. $$ \sqrt{3 y+6}=\sqrt{7 y-6} $$