# 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 $\frac{1}{\sqrt{{x}^{2}}}$ 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?

Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
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
hi
Loga
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
how did you get the value of 2000N.What calculations are needed to arrive at it
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