# 5.8 Sample test: exponents

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This module provides a sample test over exponents.

$x^{-6}$

$x^{0}$

$x^{\left(\frac{1}{8}\right)}$

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

$\frac{1}{{a}^{-3}}$

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

$\left(\frac{1}{2}\right)^{-x}$

$-2^{2}$

$-2^{3}$

$-2^{-1}$

$-9^{\left(\frac{1}{2}\right)}$

$-8^{\left(\frac{1}{2}\right)}$

$y^{\left(\frac{1}{4}\right)}y^{\left(\frac{3}{4}\right)}$

$\frac{{4x}^{4}{y}^{5}z}{6{\text{wxy}}^{-3}{z}^{3}}$

$x^{\left(\frac{1}{2}\right)}^{3}$

$x^{\left(\frac{1}{2}\right)}^{2}$

${x}^{\frac{6}{3}}$

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

$(4\times 9)^{\left(\frac{1}{2}\right)}$

$4^{\left(\frac{1}{2}\right)}9^{\left(\frac{1}{2}\right)}$

Give an algebraic formula that gives the generalization for #18-19.

Solve for $x$ :

$8^{x}=64$

$8^{x}=8$

$8^{x}=1$

$8^{x}=2$

$8^{x}=\frac{1}{8}$

$8^{x}=\frac{1}{64}$

$8^{x}=\frac{1}{2}$

$8^{x}=0$

Rewrite $\frac{1}{\sqrt[3]{{x}^{2}}}$ as xsomething.

Solve for $x$ :

$2^{(x+3)}2^{(x+4)}=2$

${3}^{\left({x}^{2}\right)}$ = ${\left(\frac{1}{9}\right)}^{3x}$

A friend of yours is arguing that $\mathrm{x⅓}$ should be defined to mean something to do with “fractions, or division, or something.” You say “No, it means _____ instead.” He says “That’s a crazy definition!” Give him a convincing argument why it should mean what you said it means.

On October 1, I place 3 sheets of paper on the ground. Each day thereafter, I count the number of sheets on the ground, and add that many again. (So if there are 5 sheets, I add 5 more.) After I add my last pile on Halloween (October 31), how many sheets are there total?

• ## A

Give me the answer as a formula.
• ## B

Plug that formula into your calculator to get a number.
• ## C

If one sheet of paper is $\frac{1}{\text{250}}$ inches thick, how thick is the final pile?

## Depreciation

The Web site www.bankrate.com defines depreciation as “the decline in a car’s value over the course of its useful life” (and also as “something new-car buyers dread”). The site goes on to say:

Let’s start with some basics. Here’s a standard rule of thumb about used cars. A car loses 15 percent to 20 percent of its value each year.

For the purposes of this problem, let’s suppose you buy a new car for exactly \$10,000, and it loses only 15% of its value every year.

• ## A

How much is your car worth after the first year?
• ## B

How much is your car worth after the second year?
• ## C

How much is your car worth after the nth year?
• ## D

How much is your car worth after ten years? (This helps you understand why new-car buyers dread depreciation.)

Draw a graph of $y=23^{x}$ . Make sure to include negative and positive values of $x$ .

Draw a graph of $y=\left(\frac{1}{3}\right)^{x}-3$ . Make sure to include negative and positive values of $x$ .

What are the domain and range of the function you graphed in number 36?

## Extra credit:

We know that $(a+b)^{2}$ is not, in general, the same as $a^{2}+b^{2}$ . But under what circumstances, if any, are they the same?

Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
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