Chapter 8

Write the expression as a single power of the base. (Lesson 8.1) $$y^{3} \cdot y$$

Use a calculator to perform the indicated operation. Write the result in scientific notation and in decimal form. $$ 6,000,000 \cdot 324,000 $$

Solve the equation. Round the result to the nearest hundredth. Check the rounded solution. $$3 y-5=11$$

Simplify the expression. \(\left(6 z^{4}\right)^{2} \cdot z^{3}\)

Rewrite the expression with positive exponents. $$ \frac{y^{4}}{x^{-10}} $$

Evaluate the expression for the given value of the variable(s). $$x^{2}-12 when x=6$$

Simplify the expression. Use only positive exponents. $$ \frac{4 x y}{2 x^{-1} y^{-3}} \cdot\left(\frac{2 x y^{2}}{3 x y}\right)^{-2} $$

Write the expression as a single power of the base. (Lesson 8.1) $$r^{2} \cdot r^{4}$$

Use a calculator to perform the indicated operation. Write the result in scientific notation and in decimal form. $$ \left(2.79 \times 10^{-4}\right)\left(3.94 \times 10^{9}\right) $$

Solve the equation. Round the result to the nearest hundredth. Check the rounded solution. $$13 t+8=2$$

Simplify the expression. \(2 x^{3} \cdot(-3 x)^{2}\)

Rewrite the expression with positive exponents. $$ \frac{9 x^{-3}}{y^{-1}} $$

Evaluate the expression for the given value of the variable(s). $$49-4 w when w=2$$

Use the example on the previous page as a model. From 1994 to 1998 the sales for a clothing store increased by about the same percent each year. The sales \(S\) (in millions of dollars) for year \(t\) can be modeled by \(S=3723\left(\frac{6}{5}\right)^{t}\) where \(t=0\) corresponds to 1994 . Find the ratio of 1998 sales to 1995 sales.

Write the expression as a single power of the base. (Lesson 8.1) $$a^{9} \cdot a^{4}$$

Use a calculator to perform the indicated operation. Write the result in scientific notation and in decimal form. $$ \frac{3,940,000}{0.0002} $$

Solve the equation. Round the result to the nearest hundredth. Check the rounded solution. $$14-6 r=-17$$

Simplify the expression. \(4 x \cdot\left(-x \cdot x^{3}\right)^{2}\)

Rewrite the expression with positive exponents. $$ (4 x)^{-3} $$

Evaluate the expression for the given value of the variable(s). $$100-r s when r=4, s=7$$

Use the example on the previous page as a model. The average salary \(s\) (in thousands) for a professional baseball player in the United States can be modeled by \(s=136(1.18)^{t}\) where \(t=0\) represents the year \(1980 .\) Find the ratio of the average salary in 1985 to the average salary in \(1990 .\)

Write the fraction in simplest form. (Skills Review p. 763) $$\frac{25}{100}$$

Use a calculator to perform the indicated operation. Write the result in scientific notation and in decimal form. $$ \frac{6.45 \times 10^{-6}}{4.3 \times 10^{5}} $$

Solve the equation. Round the result to the nearest hundredth. Check the rounded solution. $$11 k+12=-9$$

Simplify the expression. \(\left(a b c^{2}\right)^{3} \cdot a b\)

Rewrite the expression with positive exponents. $$ (3 x y)^{-2} $$

Evaluate the expression for the given value of the variable(s). $$b^{2}-4 a c when a=1, b=5, c=3$$

Use the example on the previous page as a model. The average weight \(w\) (in pounds) of an Atlantic cod can be modeled by \(w=1.21(1.42)^{t}\) where \(t\) is the age of the fish (in years). Find the ratio of the weight of a 5 -year-old cod to the weight of a 2 -year-old cod.

Write the fraction in simplest form. (Skills Review p. 763) $$\frac{215}{645}$$

Use a calculator to perform the indicated operation. Write the result in scientific notation and in decimal form. $$ (0.000094)^{3} $$

Solve the equation. Round the result to the nearest hundredth. Check the rounded solution. $$-7 x-7=-6$$

Simplify the expression. \(\left(5 y^{2}\right)^{3} \cdot\left(y^{3}\right)^{2}\)

Rewrite the expression with positive exponents. $$ \left(6 x^{-3}\right)^{3} $$

Use the example on the previous page as a model. You memorized a list of 200 Spanish vocabulary words. Unfortunately, each week you forget one fifth of the words you knew the previous week. The number of Spanish words \(S\) you remember after \(n\) weeks can be modeled by: \(S=200\left(\frac{4}{5}\right)^{n}\) Copy and complete the table showing the number of words you remember after \(n\) weeks. $$ \begin{array}{|c|c|c|c|c|c|c|c|} \hline \text { Weeks } & {n} & {0} & {1} & {2} & {3} & {4} & {5} & {6} \\ \hline \text { Words } & {S} & {?} & {?} & {?} & {?} & {?} & {?} & {?} \\ \hline \end{array} $$

Solve the equation. Round the result to the nearest hundredth. $$1.29 x=5.22 x+3.61$$

Write the fraction in simplest form. (Skills Review p. 763) $$\frac{53}{424}$$

Write the equation in standard form with integer coefficients. $$y=-8 x+4$$

Rewrite the expression with positive exponents. $$ \frac{1}{(4 x)^{-5}} $$

Give a reason for each step to show that the definitions of zero and negative exponents hold true for the properties of exponents. $$ \begin{aligned} &a^{0}=a^{n-n}\\\ &=\frac{a^{n}}{a^{n}}\\\ &=1 \end{aligned} $$

Write the fraction in simplest form. (Skills Review p. 763) $$\frac{71}{355}$$

Write the number in decimal form. The distance that light travels in one year is \(9.46 \times 10^{12}\) kilometers -

Write the equation in standard form with integer coefficients. $$y=5 x-2$$

Give a reason for each step to show that the definitions of zero and negative exponents hold true for the properties of exponents. $$ \begin{aligned} a^{-n} &=a^{n-2 n} \\ &=\frac{a^{n}}{a^{2 n}} \\ &=\frac{a^{n}}{a^{n} \cdot a^{n}} \\ &=\frac{1}{a^{n}} \end{aligned} $$

Solve the equation. Round the result to the nearest hundredth. $$10.52 x+1.15=-1.12 x-6.35$$

Write the number in decimal form. The length of a dust mite is \(9.8 \times 10^{-4}\) foot.

The power generated by a windmill can be modeled by \(w=0.015 s^{3},\) where \(w\) is the power measured in watts and s is the wind speed in miles per hour. Find the ratio of the power generated when the wind speed is 20 miles per hour to the power generated when the wind speed is 10 miles per hour.

A piece of notebook paper is about 0.0032 inch thick. If you begin with a stack consisting of a single sheet and double the stack 25 times, how thick will the stack be? \(H I N T:\) You will need to write and solve an exponential equation.

Solve the equation. Round the result to the nearest hundredth. $$8.75 x+2.16=18.28 x-6.59$$

Write the number in scientific notation. At the end of 1999 the population of the world was estimated at 6,035,000,000.

Write the equation in standard form with integer coefficients. $$y=-\frac{2}{5} x$$