91Ó°ÊÓ

In Exercises \(85-94,\) simplify using properties of exponents. $$\left(125 x^{9} y^{6}\right)^{1 / 3}$$

insert either \(<\) or \(>\) in the box between the numbers to make the statement true. $$ -\pi \square-3.5 $$

In Exercises \(85-94,\) simplify using properties of exponents. $$\frac{\left(3 y^{2 / 4}\right)^{3}}{y^{1 / 12}}$$

In Exercises 85-94, factor and simplify each algebraic expression. $$(4 x-1)^{1 / 2}-\frac{1}{3}(4 x-1)^{3 / 2}$$

insert either \(<\) or \(>\) in the box between the numbers to make the statement true. $$ -\frac{3.14}{2} \square-\frac{\pi}{2} $$

Explain how to multiply two binomials using the FOIL method. Give an example with your explanation.

Use \(10^{12}\) for one trillion and \(2.8 \times 10^{8}\) for the U.S. population in 2000 to solve. In \(2000,\) the government collected approximately \(\$ 1.9\) trillion in taxes. What was the per capita tax burden, or the amount that each U.S. citizen paid in taxes? Round to the nearest hundred dollars.

A business that manufactures small alarm clocks has a weekly fixed cost of \(\$ 5000 .\) The average cost per clock for the business to manufacture \(x\) clocks is described by $$ \frac{0.5 x+5000}{x} $$ a. Find the average cost when \(x=100,1000,\) and \(10,000\) b. Like all other businesses, the alarm clock manufacturer must make a profit. To do this, each clock must be sold for at least \(50 \notin\) more than what it costs to manufacture. Due to competition from a larger company, the clocks can be sold for \(\$ 1.50\) each and no more. Our small manufacturer can only produce 2000 clocks weekly. Does this business have much of a future? Explain.

In Exercises 85-94, factor and simplify each algebraic expression. $$-8(4 x+3)^{-2}+10(5 x+1)(4 x+3)^{-1}$$

In Exercises \(85-94,\) simplify using properties of exponents. $$\frac{\left(2 y^{1 / 5}\right)^{4}}{y^{3 / 10}}$$