# 6.7 Integer exponents and scientific notation  (Page 7/10)

 Page 7 / 10

Coin production In 1942, the U.S. Mint produced 154,500,000 nickels. Write 154,500,000 in scientific notation.

$1.545\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{8}$

Distance The distance between Earth and one of the brightest stars in the night star is 33.7 light years. One light year is about 6,000,000,000,000 (6 trillion), miles.

1. Write the number of miles in one light year in scientific notation.
2. Use scientific notation to find the distance between Earth and the star in miles. Write the answer in scientific notation.

Debt At the end of fiscal year 2015 the gross United States federal government debt was estimated to be approximately $18,600,000,000,000 ($18.6 trillion), according to the Federal Budget. The population of the United States was approximately 300,000,000 people at the end of fiscal year 2015.

1. Write the debt in scientific notation.
2. Write the population in scientific notation.
3. Find the amount of debt per person by using scientific notation to divide the debt by the population. Write the answer in scientific notation.

$1.86\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{13}$ $3\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{8}$ $6.2\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{4}$

## Writing exercises

1. Explain the meaning of the exponent in the expression ${2}^{3}$ .
2. Explain the meaning of the exponent in the expression ${2}^{-3}$ .

When you convert a number from decimal notation to scientific notation, how do you know if the exponent will be positive or negative?

## Self check

After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

Overall, after looking at the checklist, do you think you are well-prepared for the next section? Why or why not?

## Section 6.1 Add and Subtract Polynomials

Identify Polynomials, Monomials, Binomials and Trinomials

In the following exercises, determine if each of the following polynomials is a monomial, binomial, trinomial, or other polynomial.

$11{c}^{4}-23{c}^{2}+1$
$9{p}^{3}+6{p}^{2}-p-5$
$\frac{3}{7}x+\frac{5}{14}$
10
$2y-12$

${a}^{2}-{b}^{2}$
$24{d}^{3}$
${x}^{2}+8x-10$
${m}^{2}{n}^{2}-2mn+6$
$7{y}^{3}+{y}^{2}-2y-4$

binomial monomial trinomial trinomial other polynomial

Determine the Degree of Polynomials

In the following exercises, determine the degree of each polynomial.

1. $3{x}^{2}+9x+10$
2. $14{a}^{2}bc$
3. $6y+1$
4. ${n}^{3}-4{n}^{2}+2n-8$
5. $-19$
1. $5{p}^{3}-8{p}^{2}+10p-4$
2. $-20{q}^{4}$
3. ${x}^{2}+6x+12$
4. $23{r}^{2}{s}^{2}-4rs+5$
5. 100

3 4 2 4 0

Add and Subtract Monomials

In the following exercises, add or subtract the monomials.

${\phantom{\rule{0.2em}{0ex}}\text{5y}}^{\text{3}}+8{y}^{3}$

$-14k+19k$

$5k$

$12q-\left(-6q\right)$

$-9c-18c$

$-27c$

$\text{12x}-4y-9x$

$3{m}^{2}+7{n}^{2}-3{m}^{2}$

$7{n}^{2}$

$6{x}^{2}y-4x+8x{y}^{2}$

$\text{13a}+b$

$\text{13a}+b$

Add and Subtract Polynomials

In the following exercises, add or subtract the polynomials.

$\left(5{x}^{2}+12x+1\right)+\left(6{x}^{2}-8x+3\right)$

$\left(9{p}^{2}-5p+3\right)+\left(4{p}^{2}-4\right)$

$13{p}^{2}-5p-1$

$\left(10{m}^{2}-8m-1\right)-\left(5{m}^{2}+m-2\right)$

$\left(7{y}^{2}-8y\right)-\left(y-4\right)$

$7{y}^{2}-9y+4$

Subtract
$\left(3{s}^{2}+10\right)\phantom{\rule{0.2em}{0ex}}\text{from}\phantom{\rule{0.2em}{0ex}}\left(15{s}^{2}-2s+8\right)$

Find the sum of $\left({a}^{2}+6a+9\right)\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}\left(5{a}^{3}-7\right)$

$5{a}^{3}+{a}^{2}+6a+2$

Evaluate a Polynomial for a Given Value of the Variable

In the following exercises, evaluate each polynomial for the given value.

Evaluate $3{y}^{2}-y+1$ when:

1. $y=5$
2. $y=-1$
3. $y=0$

Evaluate $10-12x$ when:

1. $x=3$
2. $x=0$
3. $x=-1$

$-26$ 10 22

Randee drops a stone off the 200 foot high cliff into the ocean. The polynomial $-16{t}^{2}+200$ gives the height of a stone $t$ seconds after it is dropped from the cliff. Find the height after $t=3$ seconds.

A manufacturer of stereo sound speakers has found that the revenue received from selling the speakers at a cost of p dollars each is given by the polynomial $-4{p}^{2}+460p.$ Find the revenue received when $p=75$ dollars.

12,000

#### Questions & Answers

will every polynomial have finite number of multiples?
a=# of 10's. b=# of 20's; a+b=54; 10a + 20b=$910; a=54 -b; 10(54-b) + 20b=$910; 540-10b+20b=$910; 540+10b=$910; 10b=910-540; 10b=370; b=37; so there are 37 20's and since a+b=54, a+37=54; a=54-37=17; a=17, so 17 10's. So lets check. $740+$170=$910. David Reply . A cashier has 54 bills, all of which are$10 or $20 bills. The total value of the money is$910. How many of each type of bill does the cashier have?
whats the coefficient of 17x
the solution says it 14 but how i thought it would be 17 im i right or wrong is the exercise wrong
Dwayne
17
Melissa
wow the exercise told me 17x solution is 14x lmao
Dwayne
thank you
Dwayne
A private jet can fly 1,210 miles against a 25 mph headwind in the same amount of time it can fly 1,694 miles with a 25 mph tailwind. Find the speed of the jet
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?
Ethan and Leo start riding their bikes at the opposite ends of a 65-mile bike path. After Ethan has ridden 1.5 hours and Leo has ridden 2 hours, they meet on the path. Ethan’s speed is 6 miles per hour faster than Leo’s speed. Find the speed of the two bikers.
Nathan walked on an asphalt pathway for 12 miles. He walked the 12 miles back to his car on a gravel road through the forest. On the asphalt he walked 2 miles per hour faster than on the gravel. The walk on the gravel took one hour longer than the walk on the asphalt. How fast did he walk on the gravel?
Mckenzie
Nancy took a 3 hour drive. She went 50 miles before she got caught in a storm. Then she drove 68 miles at 9 mph less than she had driven when the weather was good. What was her speed driving in the storm?
Mr Hernaez runs his car at a regular speed of 50 kph and Mr Ranola at 36 kph. They started at the same place at 5:30 am and took opposite directions. At what time were they 129 km apart?
90 minutes
Melody wants to sell bags of mixed candy at her lemonade stand. She will mix chocolate pieces that cost $4.89 per bag with peanut butter pieces that cost$3.79 per bag to get a total of twenty-five bags of mixed candy. Melody wants the bags of mixed candy to cost her $4.23 a bag to make. How many bags of chocolate pieces and how many bags of peanut butter pieces should she use? Jake Reply enrique borrowed$23,500 to buy a car he pays his uncle 2% interest on the $4,500 he borrowed from him and he pays the bank 11.5% interest on the rest. what average interest rate does he pay on the total$23,500
13.5
Pervaiz
Amber wants to put tiles on the backsplash of her kitchen counters. She will need 36 square feet of tiles. She will use basic tiles that cost $8 per square foot and decorator tiles that cost$20 per square foot. How many square feet of each tile should she use so that the overall cost of the backsplash will be \$10 per square foot?
The equation P=28+2.54w models the relation between the amount of Randy’s monthly water bill payment, P, in dollars, and the number of units of water, w, used. Find the payment for a month when Randy used 15 units of water.
Bridget
help me understand graphs
what kind of graphs?
bruce
function f(x) to find each value
Marlene
I am in algebra 1. Can anyone give me any ideas to help me learn this stuff. Teacher and tutor not helping much.
Marlene
Given f(x)=2x+2, find f(2) so you replace the x with the 2, f(2)=2(2)+2, which is f(2)=6
Melissa
if they say find f(5) then the answer would be f(5)=12
Melissa
I need you to help me Melissa. Wish I can show you my homework
Marlene
How is f(1) =0 I am really confused
Marlene
what's the formula given? f(x)=?
Melissa
It shows a graph that I wish I could send photo of to you on here
Marlene
Which problem specifically?
Melissa
which problem?
Melissa
I don't know any to be honest. But whatever you can help me with for I can practice will help
Marlene
I got it. sorry, was out and about. I'll look at it now.
Melissa
Thank you. I appreciate it because my teacher assumes I know this. My teacher before him never went over this and several other things.
Marlene
I just responded.
Melissa
Thank you
Marlene
-65r to the 4th power-50r cubed-15r squared+8r+23 ÷ 5r
State the question clearly please
Rich
write in this form a/b answer should be in the simplest form 5%
convert to decimal 9/11
August
0.81818
Rich
5/100 = .05 but Rich is right that 9/11 = .81818
Melissa