91Ó°ÊÓ

Solve each equation by hand. Do not use a calculator. $$4 x^{3 / 2}+5=21$$

Use positive rational exponents to rewrite each expression. Assume variables represent positive numbers. $$\sqrt[5]{x^{2}}$$

Find all complex solutions for each equation by hand. Do not use a calculator. $$\frac{1}{x+2}+\frac{3}{x+7}=\frac{5}{x^{2}+9 x+14}$$

Explain how the graph of \(f\) can be obtained from the graph of \(y=\frac{1}{x}\) or \(y=\frac{1}{x^{2}}\) Draw a sketch of the graph of \(f\) by hand. Then generate an accurate depiction of the graph with a graphing calculator. Finally, give the domain and range. $$f(x)=\frac{1}{x^{2}}-2$$

Use positive rational exponents to rewrite each expression. Assume variables represent positive numbers. $$(\sqrt[4]{y})^{-3}$$

Solve each equation by hand. Do not use a calculator. $$x^{-2}+3 x^{-1}+2=0$$

Solve each equation by hand. Do not use a calculator. $$2 x^{-2}-x^{-1}=3$$

Use positive rational exponents to rewrite each expression. Assume variables represent positive numbers. $$(\sqrt[3]{y^{2}})^{-5}$$

Find all complex solutions for each equation by hand. Do not use a calculator. $$\frac{1}{x+3}+\frac{4}{x+5}=\frac{2}{x^{2}+8 x+15}$$

Explain how the graph of \(f\) can be obtained from the graph of \(y=\frac{1}{x}\) or \(y=\frac{1}{x^{2}}\) Draw a sketch of the graph of \(f\) by hand. Then generate an accurate depiction of the graph with a graphing calculator. Finally, give the domain and range. $$f(x)=\frac{1}{x^{2}}+3$$