Chapter 8

DECIMAL FORM Rewrite in decimal form. $$ 8.6521 \times 10^{3} $$

Use the power of a product property to simplify the expression. $$ \left(x^{3} y^{8}\right)^{5} $$

Evaluate the exponential expression. Write fractions in simplest form $$-6^{0} \cdot \frac{1}{3^{-2}}$$

Evaluate the expression. Write fractions in simplest form. $$ \frac{8^{3}}{8^{1}} $$

Classify the model as exponential growth or exponential decay. Identify the growth or decay factor and the percent of increase or decrease per time period. $$y=112(0.4)^{t}$$

DECIMAL FORM Rewrite in decimal form. $$ 4.65 \times 10^{-4} $$

Use the power of a product property to simplify the expression. $$ \left(-2 x^{3}\right)^{3} $$

Evaluate the exponential expression. Write fractions in simplest form $$2^{-3} \cdot 2^{2}$$

Evaluate the expression. Write fractions in simplest form. $$ \frac{(-3)^{6}}{-3^{6}} $$

Write an exponential growth model. A business had a \(\$ 10,000\) profit in \(1990 .\) Then the profit increased by \(25 \%\) per year for the next 10 years.

Classify the model as exponential growth or exponential decay. Identify the growth or decay factor and the percent of increase or decrease per time period. $$y=9\left(\frac{2}{5}\right)^{t}$$

DECIMAL FORM Rewrite in decimal form. $$ 6.002 \times 10^{-6} $$

Write your answer as a power or as a product of powers. $$ 3^{4} \cdot 3^{6} $$

Evaluate the exponential expression. Write fractions in simplest form $$8^{3} \cdot 0^{-1}$$

Evaluate the expression. Write fractions in simplest form. $$ \frac{(-3)^{9}}{(-3)^{9}} $$

Write an exponential growth model. A business had a \(\$ 20,000\) profit in \(1990 .\) Then the profit increased by \(20 \%\) per year for the next 10 years.

Classify the model as exponential growth or exponential decay. Identify the growth or decay factor and the percent of increase or decrease per time period. $$y=97(1.01)^{t}$$

DECIMAL FORM Rewrite in decimal form. $$ 4.332 \times 10^{8} $$

Write your answer as a power or as a product of powers. $$ 5^{8} \cdot 5^{3} $$

Evaluate the exponential expression. Write fractions in simplest form $$7^{4} \cdot 7^{-4}$$

Evaluate the expression. Write fractions in simplest form. $$ \frac{3^{3}}{3^{-4}} $$

Use the following information. The concentration of aspirin in a person's bloodstream can be modeled by the equation \(y=A(0.8)^{t},\) where \(y\) represents the concentration of aspirin in a person's bloodstream in milligrams (mg), \(A\) represents the amount of aspirin taken, and \(t\) represents the number of hours since the medication was taken. Find the amount of aspirin remaining in a person's bloodstream at the given dosage. Dosage: \(250 \mathrm{mg}\) Time: after 2 hours

DECIMAL FORM Rewrite in decimal form. $$ 1.00012 \times 10^{8} $$

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

Evaluate the exponential expression. Write fractions in simplest form $$8^{-7} \cdot 8^{7}$$

Evaluate the expression. Write fractions in simplest form. $$ \frac{8^{3} \cdot 8^{2}}{8^{5}} $$

A population of 30 mice is released in a wildlife region. The population doubles each year for 4 years. What is the population after 4 years?

Use the following information. The concentration of aspirin in a person's bloodstream can be modeled by the equation \(y=A(0.8)^{t},\) where \(y\) represents the concentration of aspirin in a person's bloodstream in milligrams (mg), \(A\) represents the amount of aspirin taken, and \(t\) represents the number of hours since the medication was taken. Find the amount of aspirin remaining in a person's bloodstream at the given dosage. Dosage: \(500 \mathrm{mg}\) Time: after 3.5 hours

DECIMAL FORM Rewrite in decimal form. $$ 1.1098 \times 10^{10} $$

Write your answer as a power or as a product of powers. $$ \left(7^{4}\right)^{2} $$

Evaluate the exponential expression. Write fractions in simplest form $$-4 \cdot(-4)^{-1}$$

Evaluate the expression. Write fractions in simplest form. $$ \frac{5 \cdot 5^{4}}{5^{8}} $$

Use the following information. The concentration of aspirin in a person's bloodstream can be modeled by the equation \(y=A(0.8)^{t},\) where \(y\) represents the concentration of aspirin in a person's bloodstream in milligrams (mg), \(A\) represents the amount of aspirin taken, and \(t\) represents the number of hours since the medication was taken. Find the amount of aspirin remaining in a person's bloodstream at the given dosage. Dosage: \(750 \mathrm{mg}\) Time: after 5 hours

SCIENTIFIC NOTATION Rewrite in scientific notation. $$ 0.05 $$

Write your answer as a power or as a product of powers. $$ x \cdot x^{6} $$

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

Evaluate the expression. Write fractions in simplest form. $$ \left(\frac{3}{4}\right)^{2} $$

You buy a used truck in 1996 for \(\$ 10,500\). Each year the truck depreciates by \(10 \% .\) Write an exponential decay model to represent this situation. Then estimate the value of the truck in 10 years.

SCIENTIFIC NOTATION Rewrite in scientific notation. $$ 95.2 $$

Write your answer as a power or as a product of powers. $$ (3 \cdot 7)^{2} $$

Evaluate the exponential expression. Write fractions in simplest form $$\left(-3^{-2}\right)^{-1}$$

Evaluate the expression. Write fractions in simplest form. $$ \left(\frac{6}{2}\right)^{3} $$

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. Write an exponential decay model showing the number of teams \(N\) left in the tournament after round \(t.\)

SCIENTIFIC NOTATION Rewrite in scientific notation. $$ 0.0422 $$

Write your answer as a power or as a product of powers. $$ (2 x)^{2} $$

Evaluate the exponential expression. Write fractions in simplest form $$11 \cdot 11^{-1}$$

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

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. How many teams remain after 3 rounds? after 4 rounds?

SCIENTIFIC NOTATION Rewrite in scientific notation. $$ 370.207 $$

Write your answer as a power or as a product of powers. $$ (-5 a)^{3} $$