Chapter 8

Write the number in scientific notation. $$ 6.900 .000 $$

Use the quotient of powers property to simplify the expression. $$ \frac{m^{5}}{m^{11}} $$

Tell whether the graph of the function contains the point \((0,1) .\) Explain your answer. $$y=2(3)^{x}$$

Use the power of a power property to write the expression as a single power of the base. \(\left(y^{4}\right)^{5}\)

Evaluate the expression without using a calculator. $$ \left(9^{-1}\right)^{2} $$

Classify the model as exponential growth or exponential decay. $$ y=55(3)^{t} $$

Write an exponential function to model the situation. Tell what each variable represents. Your salary of $25,000 increases 7% each year.

Write the number in scientific notation. $$ 39.6 $$

Use the quotient of powers property to simplify the expression. $$ \frac{x^{7} \cdot x}{x^{2}} $$

Tell whether the graph of the function contains the point \((0,1) .\) Explain your answer. $$y=5(7)^{x}$$

Use the power of a product property to simplify the expression. \((3 \cdot 4)^{3}\)

Use a calculator to evaluate the expression. Round your answer to the nearest ten thousandth. $$ 5^{-4} $$

Classify the model as exponential growth or exponential decay. $$ y=55(0.3)^{t} $$

Write an exponential function to model the situation. Tell what each variable represents. A population of 310,000 increases by 15% each year.

Use the power of a quotient property to simplify the expression. $$ \left(\frac{1}{2}\right)^{5} $$

Write the number in scientific notation. $$ 0.99 $$

Tell whether the graph of the function contains the point \((0,1) .\) Explain your answer. $$y=\left(\frac{1}{8}\right)^{x}$$

Use the power of a product property to simplify the expression. \((2 n)^{4}\)

Use a calculator to evaluate the expression. Round your answer to the nearest ten thousandth. $$ 7^{-1} \cdot 7^{-3} $$

Identify the initial amount and the decay factor in the exponential function. $$ y=10(0.2)^{t} $$

Write an exponential function to model the situation. Tell what each variable represents. An annual benefit concert attendance of 10,000 increases by 5% each year.

Use the power of a quotient property to simplify the expression. $$ \left(\frac{3}{5}\right)^{3} $$

Write the number in scientific notation. $$ 0.0003 $$

Tell whether the graph of the function contains the point \((0,1) .\) Explain your answer. $$y=\left(\frac{3}{4}\right)^{x}$$

Use the power of a product property to simplify the expression. \((3 p q)^{3}\)

Use a calculator to evaluate the expression. Round your answer to the nearest ten thousandth. $$ \left(8^{2}\right)^{-1} $$

Identify the initial amount and the decay factor in the exponential function. $$ y=18(0.11)^{t} $$

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

Use the power of a quotient property to simplify the expression. $$ \left(\frac{-4}{3}\right)^{4} $$

Write the number in scientific notation. $$ 0.0205 $$

Tell whether the graph of the function contains the point \((0,1) .\) Explain your answer. $$y=7\left(\frac{1}{5}\right)^{x}$$

Copy and complete the statement. \(3^{2} \cdot 3^{?}=3^{7}\)

Use a calculator to evaluate the expression. Round your answer to the nearest ten thousandth. $$ (3 \cdot 4)^{-3} $$

Identify the initial amount and the decay factor in the exponential function. $$ y=2\left(\frac{1}{4}\right)^{t} $$

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

Use the power of a quotient property to simplify the expression. $$ \left(\frac{5}{4}\right)^{-3} $$

Perform the indicated operation. Write the result in scientific notation. $$ \left(5 \times 10^{6}\right)\left(6 \times 10^{-2}\right) $$

Tell whether the graph of the function contains the point \((0,1) .\) Explain your answer. $$y=4\left(\frac{4}{9}\right)^{x}$$

Copy and complete the statement. \(5^{?} \cdot 5^{8}=5^{9}\)

Rewrite the expression with positive exponents. $$ m^{-2} $$

Identify the initial amount and the decay factor in the exponential function. $$ y=0.5\left(\frac{5}{8}\right)^{t} $$

Write an exponential growth model for the profit. A business had a $15,000 profit in 1990. Then the profit increased by 30% per year for the next 15 years.

Use the power of a quotient property to simplify the expression. $$ \left(\frac{-5}{m}\right)^{2} $$

Perform the indicated operation. Write the result in scientific notation. $$ \frac{1.4 \times 10^{-3}}{7 \times 10^{7}} $$

Make a table of values for the exponential function. Use \(x\) -values of \(-2,-1,0,1,2,\) and 3. $$y=3^{x}$$

Copy and complete the statement. \(4^{10} \cdot 4^{8}=4^{?}\)

Rewrite the expression with positive exponents. $$ a^{5} b^{-8} $$

Write an exponential model to represent the situation. Tell what each variable represents. A 25,000 dollar car depreciates at a rate of \(9 \%\) each year.

You deposit \(\$1400\) in an account that pays 6% interest compounded yearly. Find the balance at the end of the given time period. $$5 years$$

Use the power of a quotient property to simplify the expression. $$ \left(\frac{x}{y}\right)^{6} $$