# 6.7 Integer exponents and scientific notation  (Page 6/10)

 Page 6 / 10

## Practice makes perfect

Use the Definition of a Negative Exponent

In the following exercises, simplify.

${4}^{-2}$
${10}^{-3}$

${3}^{-4}$
${10}^{-2}$

$\frac{1}{81}$ $\frac{1}{100}$

${5}^{-3}$
${10}^{-5}$

${2}^{-8}$
${10}^{-2}$

$\frac{1}{256}$ $\frac{1}{100}$

$\frac{1}{{c}^{-5}}$
$\frac{1}{{3}^{-2}}$

$\frac{1}{{c}^{-5}}$
$\frac{1}{{5}^{-2}}$

${c}^{5}$ 25

$\frac{1}{{q}^{-10}}$
$\frac{1}{{10}^{-3}}$

$\frac{1}{{t}^{-9}}$
$\frac{1}{{10}^{-4}}$

${t}^{9}$ 10000

${\left(\frac{5}{8}\right)}^{-2}$
${\left(-\frac{3m}{n}\right)}^{-2}$

${\left(\frac{3}{10}\right)}^{-2}$
${\left(-\frac{2}{cd}\right)}^{-3}$

$\frac{100}{9}$ $-\frac{{c}^{3}{d}^{3}}{8}$

${\left(\frac{4}{9}\right)}^{-3}$
${\left(-\frac{{u}^{2}}{2v}\right)}^{-5}$

${\left(\frac{7}{2}\right)}^{-3}$
${\left(-\frac{3}{x{y}^{2}}\right)}^{-3}$

$\frac{8}{343}$ $-\frac{{x}^{3}{y}^{6}}{27}$

${\left(-5\right)}^{-2}$
$\text{−}{5}^{-2}$
${\left(-\frac{1}{5}\right)}^{-2}$
$\text{−}{\left(\frac{1}{5}\right)}^{-2}$

${\left(-7\right)}^{-2}$
$-{7}^{-2}$
${\left(-\frac{1}{7}\right)}^{-2}$
$\text{−}{\left(\frac{1}{7}\right)}^{-2}$

$\frac{1}{49}$ $-\frac{1}{49}$ 49 $-49$

$\text{−}{3}^{-3}$
${\left(-\frac{1}{3}\right)}^{-3}$
$\text{−}{\left(\frac{1}{3}\right)}^{-3}$
${\left(-3\right)}^{-3}$

$\text{−}{5}^{-3}$
${\left(-\frac{1}{5}\right)}^{-3}$
$\text{−}{\left(\frac{1}{5}\right)}^{-3}$
${\left(-5\right)}^{-3}$

$-\frac{1}{125}$ $-125$ $-125$ $-\frac{1}{125}$

$3·{5}^{-1}$
${\left(3·5\right)}^{-1}$

$2·{5}^{-1}$
${\left(2·5\right)}^{-1}$

$\frac{2}{5}$ $\frac{1}{10}$

$4·{5}^{-2}$
${\left(4·5\right)}^{-2}$

$3·{4}^{-2}$
${\left(3·4\right)}^{-2}$

$\frac{3}{16}$ $\frac{1}{144}$

${m}^{-4}$
${\left({x}^{3}\right)}^{-4}$

${b}^{-5}$
${\left({k}^{2}\right)}^{-5}$

$\frac{1}{{b}^{5}}$ $\frac{1}{{k}^{10}}$

${p}^{-10}$
${\left({q}^{6}\right)}^{-8}$

${s}^{-8}$
${\left({a}^{9}\right)}^{-10}$

$\frac{1}{{s}^{8}}$ $\frac{1}{{a}^{90}}$

$7{n}^{-1}$
${\left(7n\right)}^{-1}$
${\left(-7n\right)}^{-1}$

$6{r}^{-1}$
${\left(6r\right)}^{-1}$
${\left(-6r\right)}^{-1}$

$\frac{6}{r}$ $\frac{1}{6r}$ $-\frac{1}{6r}$

${\left(3p\right)}^{-2}$
$3{p}^{-2}$
$-3{p}^{-2}$

${\left(2q\right)}^{-4}$
$2{q}^{-4}$
$-2{q}^{-4}$

$\frac{1}{16{q}^{4}}$ $\frac{2}{{q}^{4}}$ $-\frac{2}{{q}^{4}}$

Simplify Expressions with Integer Exponents

In the following exercises, simplify.

${b}^{4}{b}^{-8}$
${r}^{-2}{r}^{5}$
${x}^{-7}{x}^{-3}$

${s}^{3}·{s}^{-7}$
${q}^{-8}·{q}^{3}$
${y}^{-2}·{y}^{-5}$

$\frac{1}{{s}^{4}}$ $\frac{1}{{q}^{5}}$ $\frac{1}{{y}^{7}}$

${a}^{3}·{a}^{-3}$
$a·{a}^{3}$
$a·{a}^{-3}$

${y}^{5}·{y}^{-5}$
$y·{y}^{5}$
$y·{y}^{-5}$

1 ${y}^{6}$ $\frac{1}{{y}^{4}}$

${p}^{5}·{p}^{-2}·{p}^{-4}$

${x}^{4}·{x}^{-2}·{x}^{-3}$

$\frac{1}{x}$

$\left({w}^{4}{x}^{-5}\right)\left({w}^{-2}{x}^{-4}\right)$

$\left({m}^{3}{n}^{-3}\right)\left({m}^{-5}{n}^{-1}\right)$

$\frac{1}{{m}^{2}{n}^{4}}$

$\left(u{v}^{-2}\right)\left({u}^{-5}{v}^{-3}\right)$

$\left(p{q}^{-4}\right)\left({p}^{-6}{q}^{-3}\right)$

$\frac{1}{{p}^{5}{q}^{7}}$

$\left(-6{c}^{-3}{d}^{9}\right)\left(2{c}^{4}{d}^{-5}\right)$

$\left(-2{j}^{-5}{k}^{8}\right)\left(7{j}^{2}{k}^{-3}\right)$

$-\frac{14{k}^{5}}{{j}^{3}}$

$\left(-4{r}^{-2}{s}^{-8}\right)\left(9{r}^{4}{s}^{3}\right)$

$\left(-5{m}^{4}{n}^{6}\right)\left(8{m}^{-5}{n}^{-3}\right)$

$-\frac{40{n}^{3}}{m}$

${\left(5{x}^{2}\right)}^{-2}$

${\left(4{y}^{3}\right)}^{-3}$

$\frac{1}{64{y}^{9}}$

${\left(3{z}^{-3}\right)}^{2}$

${\left(2{p}^{-5}\right)}^{2}$

$\frac{4}{{p}^{10}}$

$\frac{{t}^{9}}{{t}^{-3}}$

$\frac{{n}^{5}}{{n}^{-2}}$

${n}^{7}$

$\frac{{x}^{-7}}{{x}^{-3}}$

$\frac{{y}^{-5}}{{y}^{-10}}$

${y}^{5}$

Convert from Decimal Notation to Scientific Notation

In the following exercises, write each number in scientific notation.

57,000

340,000

$3.4\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{5}$

8,750,000

1,290,000

$1.29\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{6}$

0.026

0.041

$4.1\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-2}$

0.00000871

0.00000103

$1.03\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-6}$

Convert Scientific Notation to Decimal Form

In the following exercises, convert each number to decimal form.

$5.2\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{2}$

$8.3\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{2}$

830

$7.5\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{6}$

$1.6\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{10}$

16,000,000,000

$2.5\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-2}$

$3.8\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-2}$

0.038

$4.13\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-5}$

$1.93\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-5}$

0.0000193

Multiply and Divide Using Scientific Notation

$\left(3\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-5}\right)\left(3\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{9}\right)$

$\left(2\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{2}\right)\left(1\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-4}\right)$

0.02

$\left(7.1\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-2}\right)\left(2.4\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-4}\right)$

$\left(3.5\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-4}\right)\left(1.6\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-2}\right)$

$5.6\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-6}$

$\frac{7\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-3}}{1\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-7}}$

$\frac{5\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-2}}{1\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-10}}$

500,000,000

$\frac{6\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{4}}{3\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-2}}$

$\frac{8\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{6}}{4\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-1}}$

20,000,000

## Everyday math

The population of the United States on July 4, 2010 was almost 310,000,000. Write the number in scientific notation.

The population of the world on July 4, 2010 was more than 6,850,000,000. Write the number in scientific notation

$6.85\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{9}$ .

The average width of a human hair is 0.0018 centimeters. Write the number in scientific notation.

The probability of winning the 2010 Megamillions lottery was about 0.0000000057. Write the number in scientific notation.

$5.7\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-10}$

In 2010, the number of Facebook users each day who changed their status to ‘engaged’ was $2\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{4}$ . Convert this number to decimal form.

At the start of 2012, the US federal budget had a deficit of more than $\text{}1.5\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{13}$ . Convert this number to decimal form.

15,000,000,000,000

The concentration of carbon dioxide in the atmosphere is $3.9\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-4}$ . Convert this number to decimal form.

The width of a proton is $1\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-5}$ of the width of an atom. Convert this number to decimal form.

0.00001

Health care costs The Centers for Medicare and Medicaid projects that consumers will spend more than $4 trillion on health care by 2017. 1. Write 4 trillion in decimal notation. 2. Write 4 trillion in scientific notation. #### Questions & Answers Tickets for a show are$70 for adults and $50 for children. For one evening performance, a total of 300 tickets were sold and the receipts totaled$17,200. How many adult tickets and how many child tickets were sold?
A 50% antifreeze solution is to be mixed with a 90% antifreeze solution to get 200 liters of a 80% solution. How many liters of the 50% solution and how many liters of the 90% solution will be used?
June needs 45 gallons of punch for a party and has 2 different coolers to carry it in. The bigger cooler is 5 times as large as the smaller cooler. How many gallons can each cooler hold?
Washing his dad’s car alone, eight-year-old Levi takes 2.5 hours. If his dad helps him, then it takes 1 hour. How long does it take the Levi’s dad to wash the car by himself?
Bruce drives his car for his job. The equation R=0.575m+42 models the relation between the amount in dollars, R, that he is reimbursed and the number of miles, m, he drives in one day. Find the amount Bruce is reimbursed on a day when he drives 220 miles.
LeBron needs 150 milliliters of a 30% solution of sulfuric acid for a lab experiment but only has access to a 25% and a 50% solution. How much of the 25% and how much of the 50% solution should he mix to make the 30% solution?
5%
Michael
hey everyone how to do algebra
Felecia answer 1.5 hours before he reaches her
I would like to solve the problem -6/2x
12x
Andrew
how
Christian
Does the x represent a number or does it need to be graphed ?
latonya
-3/x
Venugopal
-3x is correct
Atul
Arnold invested $64,000, some at 5.5% interest and the rest at 9%. How much did he invest at each rate if he received$4,500 in interest in one year?
Tickets for the community fair cost $12 for adults and$5 for children. On the first day of the fair, 312 tickets were sold for a total of $2204. How many adult tickets and how many child tickets were sold? Alpha Reply 220 gayla Three-fourths of the people at a concert are children. If there are 87 children, what is the total number of people at the concert? Tsimmuaj Reply Erica earned a total of$50,450 last year from her two jobs. The amount she earned from her job at the store was $1,250 more than four times the amount she earned from her job at the college. How much did she earn from her job at the college? Tsimmuaj Erica earned a total of$50,450 last year from her two jobs. The amount she earned from her job at the store was $1,250 more than four times the amount she earned from her job at the college. How much did she earn from her job at the college? Tsimmuaj ? Is there anything wrong with this passage I found the total sum for 2 jobs, but found why elaborate on extra If I total one week from the store *4 would = the month than the total is = x than x can't calculate 10 month of a year candido what would be wong candido 87 divided by 3 then multiply that by 4. 116 people total. Melissa the actual number that has 3 out of 4 of a whole pie candido was having a hard time finding Teddy use Matrices for the 2nd question Daniel One number is 11 less than the other number. If their sum is increased by 8, the result is 71. Find the numbers. Tsimmuaj Reply 26 + 37 = 63 + 8 = 71 gayla 26+37=63+8=71 ziad 11+52=63+8=71 Thisha how do we know the answer is correct? Thisha 23 is 11 less than 37. 23+37=63. 63+8=71. that is what the question asked for. gayla 23 +11 = 37. 23+37=63 63+8=71 Gayla by following the question. one number is 11 less than the other number 26+11=37 so 26+37=63+8=71 Gayla your answer did not fit the guidelines of the question 11 is 41 less than 52. gayla 71-8-11 =52 is this correct? Ruel let the number is 'x' and the other number is "x-11". if their sum is increased means: x+(x-11)+8 result will be 71. so x+(x-11)+8=71 2x-11+8=71 2x-3=71 2x=71+3 2x=74 1/2(2x=74)1/2 x=37 final answer tesfu just new Muwanga Amara currently sells televisions for company A at a salary of$17,000 plus a $100 commission for each television she sells. Company B offers her a position with a salary of$29,000 plus a \$20 commission for each television she sells. How televisions would Amara need to sell for the options to be equal?
yes math
Kenneth
company A 13 company b 5. A 17,000+13×100=29,100 B 29,000+5×20=29,100
gayla
need help with math to do tsi test
Toocute
me too
Christian
have you tried the TSI practice test ***tsipracticetest.com
gayla
DaMarcus and Fabian live 23 miles apart and play soccer at a park between their homes. DaMarcus rode his bike for 34 of an hour and Fabian rode his bike for 12 of an hour to get to the park. Fabian’s speed was 6 miles per hour faster than DaMarcus’s speed. Find the speed of both soccer players.
?
Ann
DaMarcus: 16 mi/hr Fabian: 22 mi/hr
Sherman