Chapter 8

Simplify the quotient. $$ \left(\frac{3}{4}\right)^{2} $$

Write the number in scientific notation. the number $$ 370.2 $$

Graph the exponential function. $$y=-5\left(\frac{1}{5}\right)^{x}$$

Simplify the expression. \((5 x)^{3}\)

Use a calculator to evaluate the expression. Round your answer to the nearest ten thousandth. $$ 2^{-5} $$

Simplify the quotient. $$ \left(\frac{-2}{3}\right)^{3} $$

What is the value of an \(\$1000\) investment after 5 years if it earns 6% annual interest compounded quarterly (four times a year). HINT: Use the compound interest formula \(A=P\left(1+\frac{r}{n}\right)^{tn}\) where A is the value of the account, P is the initial investment, r is the interest rate, n is the number of times per year the interest is compounded, and t is the time period (in years).

Write the number in scientific notation. the number $$ 0.1 $$

Graph the exponential function. $$y=2\left(\frac{2}{3}\right)^{x}$$

Simplify the expression. \((-2 d)^{6}\)

Use a calculator to evaluate the expression. Round your answer to the nearest ten thousandth. $$ 11^{-2} $$

The hourly rate of your new job is \(\$5.00\) per hour. You expect a raise of 9% at the end of each year. What will your hourly rate be at the end of your fifth year? $$\ A. \(5.45$$ $$\ B. \)7.25$$ $$\ C. \(7.69$$ $$\ D. \)9.50$$

Simplify the quotient. $$ \left(\frac{9}{6}\right)^{-1} $$

Write the number in scientific notation. the number $$ 0.05 $$

Using your graphs , describe the domain and the range of the function. $$y=4^{x}$$

Simplify the expression. \((a b)^{2}\)

Use a calculator to evaluate the expression. Round your answer to the nearest ten thousandth. $$ 5^{-1} \cdot 5^{-3} $$

Simplify the quotient. $$ \left(\frac{3}{x}\right)^{4} $$

Write the number in scientific notation. the number $$ 0.000006 $$

Using your graphs , describe the domain and the range of the function. $$y=-7^{x}$$

Simplify the expression. \((2 m n)^{6}\)

Use a calculator to evaluate the expression. Round your answer to the nearest ten thousandth. $$ 9^{-4} \cdot 9^{2} $$

Classify the model as exponential growth or exponential decay. Then identify the growth or decay factor and graph the model. $$ y=24(1.18)^{t} $$

Evaluate the expression for the given value of the variable. (Lesson 1.3) $$24+m^{2} \text { when } m=5$$

Simplify the quotient. $$ \left(\frac{-x}{2}\right)^{3} $$

Write the number in scientific notation. the number $$ 0.0422 $$

Using your graphs , describe the domain and the range of the function. $$y=4(2)^{x}$$

Simplify the expression. \((10 x y)^{2}\)

Use a calculator to evaluate the expression. Round your answer to the nearest ten thousandth. $$ \left(4^{2}\right)^{-1} $$

Classify the model as exponential growth or exponential decay. Then identify the growth or decay factor and graph the model. $$ y=14(0.98)^{t} $$

Evaluate the expression for the given value of the variable. (Lesson 1.3) $$6 x-1\quad when\quad x=1$$

Simplify the quotient. $$ \left(\frac{x}{y}\right)^{5} $$

Write the number in scientific notation. the number $$ 0.0085 $$

Using your graphs , describe the domain and the range of the function. $$y=-3(8)^{x}$$

Simplify the expression. \((-r s t)^{5}\)

Use a calculator to evaluate the expression. Round your answer to the nearest ten thousandth. $$ \left(3^{-3}\right)^{2} $$

Classify the model as exponential growth or exponential decay. Then identify the growth or decay factor and graph the model. $$ y=97(1.01)^{t} $$

Evaluate the expression for the given value of the variable. (Lesson 1.3) $$3 \cdot 15 y \text { when } y=2$$

Simplify the quotient. $$ \left(\frac{8}{x}\right)^{-2} $$

Write the number in scientific notation. the number $$ 0.000459 $$

Using your graphs , describe the domain and the range of the function. $$y=\left(\frac{1}{2}\right)^{x}$$

Copy and complete the statement using \(<\) or \(>\). \((5 \cdot 6)^{4} \quad ? \quad 5 \cdot 6^{4}\)

Use a calculator to evaluate the expression. Round your answer to the nearest ten thousandth. $$ (2 \cdot 7)^{-1} $$

Classify the model as exponential growth or exponential decay. Then identify the growth or decay factor and graph the model. $$ y=112\left(\frac{2}{3}\right)^{t} $$

Evaluate the expression for the given value of the variable. (Lesson 1.3) $$1-\frac{a}{3} when\quad a=9$$

In Exercises 47 and \(48,\) find and correct the error. $$ \begin{aligned} \left(\frac{6 a}{b^{2}}\right)^{3} &=\frac{6 a^{3}}{b^{2} \cdot 3} \\ &=\frac{6 a^{3}}{b^{8}} \end{aligned} $$

Perform the indicated operation without using a calculator. Write the result in scientific notation. $$ \left(4.1 \times 10^{2}\right)\left(3 \times 10^{6}\right) $$

Using your graphs , describe the domain and the range of the function. $$y=\left(\frac{2}{5}\right)^{x}$$

Copy and complete the statement using \(<\) or \(>\). \(5^{2} \cdot 5^{3} ?(5 \cdot 5)^{6}\)

Use a calculator to evaluate the expression. Round your answer to the nearest ten thousandth. $$ (8 \cdot 3)^{-2} $$