91Ó°ÊÓ

Perform the indicated operations. $$ \frac{(\sqrt[3]{81 m n^{2}})^{2}}{(\sqrt[3]{m n})^{2}} $$

Speed of a Skidding Car. Police can estimate the speed at which a car was traveling by measuring its skid marks. The function given by $$r(L)=2 \sqrt{5 L}$$ can be used, where \(L\) is the length of a skid mark, in feet, and \(r(L)\) is the speed, in miles per hour. Find the exact speed and an estimate (to the nearest tenth mile per hour) for the speed of a car that left skid marks (a) 20 ft long; (b) 70 ft long; (c) 90 ft long. See also Exercise \(102 .\)

Simplifying Radical Expressions Use rational exponents to simplify. Write answers using radical notation, and do not use fraction exponents in any answers. $$(\sqrt[7]{x y})^{14}$$

Simplifying Radical Expressions Use rational exponents to simplify. Write answers using radical notation, and do not use fraction exponents in any answers. $$(\sqrt[3]{a b})^{15}$$

Factor completely. $$x^{2}-100$$

Perform the indicated operation and simplify. Assume that all variables represent positive real numbers. Write the answer using radical notation. $$ (r-\sqrt[4]{s^{3}})(3 r-\sqrt[5]{s}) $$

Solve. $$10-5 y>4$$

Let \(f(x)=x^{2} .\) Find each of the following. $$ f(\sqrt{2}+\sqrt{10}) $$

The absolute value of a complex number \(a+b i\) is its distance from the origin. (See the graph above.) Using the distance formula, we have \(|a+b i|=\sqrt{a^{2}+b^{2}}\) Find the absolute value of each complex number. $$|8-6 i|$$

Let \(f(x)=x^{2} .\) Find each of the following. Write the slope-intercept equation of the line that is perpendicular to the line \(y=\frac{1}{2} x-7\) and has a \(y\) -intercept of \((0,12)\)