Chapter 1

The average distance between Earth and the Sun is 92,960,000 mi. Rewrite the distance using scientific notation.

For the following exercises, simplify the expression. \(\left(\frac{9}{6} t-4\right) 2\)

For the following exercises, simplify the rational expression. \(\frac{\frac{a}{b}-\frac{b}{a}}{\frac{a+b}{a b}}\)

For the following exercises, factor the polynomials. \(14 x(x+2)^{-\frac{2}{5}}+5(x+2)^{\frac{3}{5}}\)

For the following exercises, multiply the polynomials. \((4 t-5 u)^{2}\)

For the following exercises, simplify each expression. \(\sqrt{\frac{32}{14 d}}\)

A terabyte is made of approximately 1,099,500,000,000 bytes. Rewrite in scientific notation.

For the following exercises, simplify the expression. \(6+12 b-3 \times 6 b\)

For the following exercises, simplify the rational expression. \(\frac{\frac{2 x}{3}+\frac{4 x}{7}}{\frac{x}{2}}\)

For the following exercises, factor the polynomials. \(9 y(3 y-13)^{\frac{1}{5}}-2(3 y-13)^{\frac{6}{5}}\)

For the following exercises, multiply the polynomials. \((9 m+4 n-1)(2 m+8)\)

For the following exercises, simplify each expression. \(q^{\frac{3}{2}} \sqrt{63 p}\)

The Gross Domestic Product (GDP) for the United States in the first quarter of 2014 was \(\$ 1.71496 \times 10^{13}\). Rewrite the GDP in standard notation.

For the following exercises, simplify the expression. \(18 y-2(1+7 y)\)

For the following exercises, simplify the rational expression. \(\frac{\frac{2 c}{c+2}+\frac{c-1}{c+1}}{\frac{2 c+1}{c+1}}\)

For the following exercises, factor the polynomials. \(5 z(2 z-9)^{-\frac{3}{2}}+11(2 z-9)^{-\frac{1}{2}}\)

For the following exercises, multiply the polynomials. \((4 t-x)(t-x+1)\)

One picometer is approximately \(3.397 \times 10^{-11}\) in. Rewrite this length using standard notation.

For the following exercises, simplify the expression. \(\left(\frac{4}{9}\right)^{2} \times 27 x\)

For the following exercises, simplify the rational expression. \(\frac{\frac{x}{y}-\frac{y}{x}}{\frac{x}{y}+\frac{y}{x}}\)

For the following exercises, factor the polynomials. \(6 d(2 d+3)^{-\frac{1}{6}}+5(2 d+3)^{\frac{5}{6}}\)

For the following exercises, multiply the polynomials. \(\left(b^{2}-1\right)\left(a^{2}+2 a b+b^{2}\right)\)

For the following exercises, simplify each expression. \(\sqrt{\frac{20}{121 a^{4}}}\)

The value of the services sector of the U.S. economy in the first quarter of 2012 was \(\$ 10,633.6\) billion. Rewrite this amount in scientific notation.

For the following exercises, simplify the expression. \(8(3-m)+1(-8)\)

Brenda is placing tile on her bathroom floor. The area of the floor is \(15 x^{2}-8 x-7 \mathrm{ft}^{2}\). The area of one tile is \(x^{2}-2 x+1 \mathrm{ft}^{2}\). To find the number of tiles needed, simplify the rational expression: \(\frac{15 x^{2}-8 x-7}{x^{2}-2 x+1}\) Area \(=15 x^{2}-8 x-7\)

For the following exercises, multiply the polynomials. \((4 r-d)(6 r+7 d)\)

For the following exercises, simplify each expression. \(w^{\frac{3}{2}} \sqrt{32}-w^{\frac{3}{2}} \sqrt{50}\)

For the following exercises, use a graphing calculator to simplify. Round the answers to the nearest hundredth. \(\left(\frac{12^{3} m^{33}}{4^{-3}}\right)^{2}\)

For the following exercises, simplify the expression. \(9 x+4 x(2+3)-4(2 x+3 x)\)

The area of Sandy's yard is \(25 x^{2}-625 \mathrm{ft}^{2}\). A patch of sod has an area of \(x^{2}-10 x+25\) \(\mathrm{ft}^{2}\). Divide the two areas and simplify to find how many pieces of sod Sandy needs to cover her yard.

A statue is to be placed in the center of the park. The area of the base of the statue is \(4 x^{2}+12 x+9 m^{2}\). Factor the area to find the lengths of the sides of the statue.

For the following exercises, multiply the polynomials. \((x+y)\left(x^{2}-x y+y^{2}\right)\)

For the following exercises, simplify each expression. \(\sqrt{108 x^{4}}+\sqrt{27 x^{4}}\)

For the following exercises, simplify the expression. \(5^{2}-4(3 x)\)

Aaron wants to mulch his garden. His garden is \(x^{2}+18 x+81 \mathrm{ft}^{2}\). One bag of mulch covers \(x^{2}-81 \mathrm{ft}^{2}\). Divide the expressions and simplify to find how many bags of mulch Aaron needs to mulch his garden.

At the northwest corner of the park, the city is going to install a fountain. The area of the base of the fountain is \(9 x^{2}-25 \mathrm{~m}^{2}\). Factor the area to find the lengths of the sides of the fountain.

A developer wants to purchase a plot of land to build a house. The area of the plot can be described by the following expression: \((4 x+1)(8 x-3)\) where \(x\) is measured in meters. Multiply the binomials to find the area of the plot in standard form.

For the following exercises, simplify each expression. \(\frac{\sqrt{12 x}}{2+2 \sqrt{3}}\)

For the following exercises, simplify the given expression. Write answers with positive exponents. \(\left(\frac{3^{2}}{a^{3}}\right)^{-2}\left(\frac{a^{4}}{2^{2}}\right)^{2}\)

For the following exercises, consider this scenario: Fred earns $$\$ 40$$ mowing lawns. He spends $$\$ 10$$ on \(\mathrm{mp} 3 \mathrm{~s}\), puts half of what is left in a savings account, and gets another $$\$ 5$$ for washing his neighbor's car. Write the expression that represents the number of dollars Fred keeps (and does not put in his savings account). Remember the order of operations.

For the following exercises, perform the given operations and simplify. \(\frac{x^{2}+x-6}{x^{2}-2 x-3} \cdot \frac{2 x^{2}-3 x-9}{x^{2}-x-2} \div \frac{10 x^{2}+27 x+18}{x^{2}+2 x+1}\)

A prospective buyer wants to know how much grain a specific silo can hold. The area of the floor of the silo is \((2 x+9)^{2}\). The height of the silo is \(10 x+10,\) where \(x\) is measured in feet. Expand the square and multiply by the height to find the expression that shows how much grain the silo can hold.

For the following exercises, simplify each expression. \(\sqrt{147 k^{3}}\)

For the following exercises, simplify the given expression. Write answers with positive exponents. \(\left(6^{2}-24\right)^{2} \div\left(\frac{x}{y}\right)^{-5}\)

For the following exercises, consider this scenario: Fred earns $$\$ 40$$ mowing lawns. He spends $$\$ 10$$ on \(\mathrm{mp} 3 \mathrm{~s}\), puts half of what is left in a savings account, and gets another $$\$ 5$$ for washing his neighbor's car. How much money does Fred keep?

For the following exercises, perform the given operations and simplify. \(\frac{\frac{3 y^{2}-10 y+3}{3 y^{2}+5 y-2} \cdot \frac{2 y^{2}-3 y-20}{2 y^{2}-y-15}}{y-4}\)

For the following exercises, factor the polynomials completely. \(16 x^{4}-200 x^{2}+625\)

For the following exercises, simplify each expression. \(\sqrt{125 n^{10}}\)

For the following exercises, simplify the given expression. Write answers with positive exponents. \(\frac{m^{2} n^{3}}{a^{2} c^{-3}} \cdot \frac{a^{-7} n^{-2}}{m^{2} c^{4}}\)