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

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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

In the following exercises, add or subtract the monomials.

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

$-14k+19k$

$5k$

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

$-9c-18c$

$-27c$

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

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

$7{n}^{2}$

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

$\text{13a}+b$

$\text{13a}+b$

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

3. When Jenna spent 10 minutes on the elliptical trainer and then did circuit training for20 minutes, her fitness app says she burned 278 calories. When she spent 20 minutes onthe elliptical trainer and 30 minutes circuit training she burned 473 calories. How manycalories does she burn for each minute on the elliptical trainer? How many calories doesshe burn for each minute of circuit training?
.473
Angelita
?
Angelita
John left his house in Irvine at 8:35 am to drive to a meeting in Los Angeles, 45 miles away. He arrived at the meeting at 9:50. At 3:30 pm, he left the meeting and drove home. He arrived home at 5:18.
p-2/3=5/6 how do I solve it with explanation pls
P=3/2
Vanarith
1/2p2-2/3p=5p/6
James
Cindy
4.5
Ruth
is y=7/5 a solution of 5y+3=10y-4
yes
James
Cindy
Lucinda has a pocketful of dimes and quarters with a value of $6.20. The number of dimes is 18 more than 3 times the number of quarters. How many dimes and how many quarters does Lucinda have? Rhonda Reply Find an equation for the line that passes through the point P ( 0 , − 4 ) and has a slope 8/9 . Gabriel Reply is that a negative 4 or positive 4? Felix y = mx + b Felix if negative -4, then -4=8/9(0) + b Felix -4=b Felix if positive 4, then 4=b Felix then plug in y=8/9x - 4 or y=8/9x+4 Felix Macario is making 12 pounds of nut mixture with macadamia nuts and almonds. macadamia nuts cost$9 per pound and almonds cost $5.25 per pound. how many pounds of macadamia nuts and how many pounds of almonds should macario use for the mixture to cost$6.50 per pound to make?
Nga and Lauren bought a chest at a flea market for $50. They re-finished it and then added a 350 % mark - up Makaila Reply$1750
Cindy
the sum of two Numbers is 19 and their difference is 15
2, 17
Jose
interesting
saw
4,2
Cindy
Felecia left her home to visit her daughter, driving 45mph. Her husband waited for the dog sitter to arrive and left home 20 minutes, or 13 hour later. He drove 55mph to catch up to Felecia. How long before he reaches her?
integer greater than 2 and less than 12
2 < x < 12
Felix
I'm guessing you are doing inequalities...
Felix
Actually, translating words into algebraic expressions / equations...
Felix
hi
Darianna
hello
Mister
Eric here
Eric
6
Cindy
He charges $125 per job. His monthly expenses are$1,600. How many jobs must he work in order to make a profit of at least \$2,400?
at least 20
Ayla
what are the steps?
Alicia
6.4 jobs
Grahame
32
Grahame
1600+2400= total amount with expenses. 4000/125= number of jobs needed to make that min profit of 2400. answer is 32
Orlando
He must work 32 jobs to make a profit
POP
32
Cindy
what is algebra
repeated addition and subtraction of the order of operations. i love algebra I'm obsessed.
Shemiah
hi
Krekar
Eric here. I'm a parent. 53 years old. I have never taken algebra. I want to learn.
Eric
I am 63 and never learned algebra
Cindy
One-fourth of the candies in a bag of M&M’s are red. If there are 23 red candies, how many candies are in the bag?
they are 92 candies in the bag
POP
92
Cindy