91Ó°ÊÓ

Multiply and simplify. Assume that no radicands were formed by raising negative numbers to even powers. $$ 3 \sqrt{2 x^{5}} \cdot 4 \sqrt{10 x^{2}} $$

Perform the indicated operation and simplify. Write each answer in the form \(a+b i\) $$ \frac{5-3 i}{4 i} $$

Without graphing, determine the x-intercepts of the graphs given by each of the following. $$f(x)=\left(x^{2}+30 x\right)^{1 / 2}-x-(5 x)^{1 / 2}$$

Use the laws of exponents to simplify. Do not use negative exponents in any answers. $$ x^{3 / 4} \cdot x^{1 / 3} $$

Simplify. $$ i^{38} $$

Perform the indicated operation and simplify. Assume that all variables represent positive real numbers. $$\sqrt{a^{4} b^{3} c^{4}} \sqrt[3]{a b^{2} c}$$

Each side of a regular octagon has length \(s .\) Find a formula for the distance \(d\) between the parallel sides of the octagon.

Perform the indicated operation and simplify. Assume that all variables represent positive real numbers. $$\frac{\sqrt[4]{x^{2} y^{3}}}{\sqrt[3]{x y}}$$

Use rational exponents to simplify. Do not use fraction exponents in the final answer. $$ (\sqrt[7]{x y})^{14} $$

To prepare for Section 11.1 , review solving quadratic equations (Chapter \(6)\) Solve. $$ 15 x^{2}=14 x+8[6.3] $$