Chapter 8

Evaluate the exponential expression. Write fractions in simplest form $$4^{0} \cdot 5^{-3}$$

Evaluate the expression. Write fractions in simplest form. $$ \left(-\frac{3}{5}\right)^{2} $$

The hourly rate of your new job is \(\$ 5.00\) per hour. You expect a raise of \(9 \%\) each year. At the end of your first year, you receive your first raise. What will your hourly rate be at the end of your fifth year? \(\begin{array}{lllll}\text { A) } \$ 5.45 & \text { (B) } \$ 7.25 & \text { C } \odot \$ 7.69 & \text { (D } \$ 7.76\end{array}\)

Use the following information. Each year in the month of March, the NCAA basketball tournament is held to determine the national champion. At the start of the tournament there are 64 teams, and after each round, one half of the remaining teams are eliminated. If a team won 6 games in a row in the tournament, does it mean that it won the national championship? Explain your reasoning.

SCIENTIFIC NOTATION Rewrite in scientific notation. $$ 700,000,000 $$

Write your answer as a power or as a product of powers. $$ \left(-2 m^{4} n^{6}\right)^{2} $$

Rewrite the expression with positive exponents. $$ x^{-5}$$

Evaluate the expression. Write fractions in simplest form. $$ \left(\frac{9}{6}\right)^{-1} $$

A summer youth camp had a declining enrollment from 1995 to \(2000 .\) The enrollment in 1995 was 320 people. Each year for the next five years, the enrollment decreased by \(2 \% .\) Copy and complete the table showing the enrollment for each year. Sketch a graph of the results. $$\begin{array}{|l|c|c|c|c|c|c|} \hline \text { Year } & 1995 & 1996 & 1997 & 1998 & 1999 & 2000 \\ \hline \text { Enrollment } & ? & ? & ? & ? & ? & ? \\ \hline \end{array}$$

SCIENTIFIC NOTATION Rewrite in scientific notation. $$ 19.314 $$

Write your answer as a power or as a product of powers. $$ \left[(-4)^{2}\right]^{3} $$

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

Simplify the expression. The simplified expression should have no negative exponents. $$\left(\frac{3}{x}\right)^{4}$$

EXTENSION: COMPOUND INTEREST What is the value of an \(\$ 8000\) investment after 5 years if it earns \(8 \%\) annual interest compounded quarterly? To solve, use the compound interest formula, \(A=P(1+i)^{n}\) where \(P\) is the original value of the investment, \(i\) is the interest rate per compounding period, \(n\) is the total number of compounding periods, and \(A\) is the value of the investment after \(n\) periods. a.) What is the interest rate per quarter? b.) How many compounding periods (quarters) are there in 5 years? c.) Use the formula \(A=P(1+i)^{n}\) to find the value of the investment after 5 years.

Use the following information. From 1894 to 1903 the number of miles of cable car track decreased by about \(10 \%\) per year. There were 302 miles of track in 1894 . Write an exponential decay model showing the number of miles \(M\) of cable car track left in year \(t.\)

SCIENTIFIC NOTATION Rewrite in scientific notation. $$ 0.008551 $$

Write your answer as a power or as a product of powers. $$ \left[(-5 x y)^{2}\right]^{5} $$

Rewrite the expression with positive exponents. $$\frac{1}{2 x^{-5}}$$

Simplify the expression. The simplified expression should have no negative exponents. $$\frac{x^{4}}{x^{5}}$$

Find the percent of a number. $$12 \% \text { of } 56$$

Use the following information. From 1894 to 1903 the number of miles of cable car track decreased by about \(10 \%\) per year. There were 302 miles of track in 1894 . Copy and complete the table. You may want to use a calculator. $$\begin{array}{|l|c|c|c|c|c|c|c|} \hline \text { Year } & 1894 & 1896 & 1898 & 1899 & 1900 & 1901 & 1903 \\ \hline \text { Miles of track } & ? & ? & ? & ? & ? & ? & ? \\ \hline \end{array}$$

SCIENTIFIC NOTATION Rewrite in scientific notation. $$ 2,730,000,000 $$

Write your answer as a power or as a product of powers. $$ \left[(5+x)^{3}\right]^{6} $$

Rewrite the expression with positive exponents. $$x^{-2} y^{4}$$

Simplify the expression. The simplified expression should have no negative exponents. $$ \left(\frac{1}{x}\right)^{5} $$

Find the percent of a number. $$75 \% \text { of } 235$$

Use the following information. From 1894 to 1903 the number of miles of cable car track decreased by about \(10 \%\) per year. There were 302 miles of track in 1894 . Sketch a graph of the results.

SCIENTIFIC NOTATION Rewrite in scientific notation. $$ 0.000459 $$

Write your answer as a power or as a product of powers. $$ \left[(2 x+3)^{3}\right]^{2} $$

Rewrite the expression with positive exponents. $$x^{4} y^{-7}$$

Simplify the expression. The simplified expression should have no negative exponents. $$ x^{3} \cdot \frac{1}{x^{2}} $$

Find the percent of a number. $$1.25 \% \text { of } 90$$

A store is having a sale on sweaters. On the first day the price of a sweater is reduced by \(20 \% .\) The price will be reduced another \(20 \%\) each day until the sweater is sold. Denise thinks that on the fifth day of the sale the sweater will be free. Is she right? Explain.

SCIENTIFIC NOTATION Rewrite in scientific notation. $$ 0.00032954 $$

Write your answer as a power or as a product of powers. $$ (3 b)^{3} \cdot b $$

Rewrite the expression with positive exponents. $$8 x^{-2} y^{-6}$$

Simplify the expression. The simplified expression should have no negative exponents. $$ x^{5} \cdot \frac{1}{x^{8}} $$

Find the percent of a number. $$200 \% \text { of } 130$$

SCIENTIFIC NOTATION Rewrite in scientific notation. $$ 88,000,000 $$

Write your answer as a power or as a product of powers. $$ 5^{3} \cdot\left(5 a^{4}\right)^{2} $$

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

Simplify the expression. The simplified expression should have no negative exponents. $$ \left(\frac{a^{9}}{a^{5}}\right)^{-1} $$

Find the percent of a number. $$2 \% \text { of } 105$$

SCIENTIFIC NOTATION Rewrite in scientific notation. $$ 0.0000288 $$

Write your answer as a power or as a product of powers. $$ 4 x \cdot\left(x \cdot x^{3}\right)^{2} $$

Rewrite the expression with positive exponents. $$\frac{1}{4 x^{-10} y^{14}}$$

Simplify the expression. The simplified expression should have no negative exponents. $$ \left(\frac{y^{2}}{y^{3}}\right)^{-2} $$

Use a graphing calculator. Make an input-output table for the equations \(y=4^{t}\) and \(y=\left(\frac{1}{4}\right)^{t} .\) Use \(-3\) \(-2,-1,0,1,2,\) and 3 as the input. Then sketch the graph of each equation.

Find the percent of a number. $$0.8 \% \text { of } 120$$

EVALUATING EXPRESSIONS Evaluate the expression without using a calculator. Write the result in scientific notation and in decimal form. $$ \left(4 \times 10^{-2}\right) \cdot\left(3 \times 10^{6}\right) $$