# 5.5 Homework: fractional exponents

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This module provides practice problems designed to develop concepts related to fractional exponents.

We have come up with the following definitions.

• $x^{0}=1$
• $x^{-a}=\frac{1}{{x}^{a}}$
• $x^{\left(\frac{a}{b}\right)}=\sqrt[b]{{x}^{a}}$

Let’s get a bit of practice using these definitions.

$100^{\left(\frac{1}{2}\right)}$

$100^{-2}$

$100^{\left(\frac{-1}{2}\right)}$

$100^{\left(\frac{3}{2}\right)}$

$100^{\left(\frac{-3}{2}\right)}$

Check all of your answers above on your calculator. If any of them did not come out right, figure out what went wrong, and fix it!

Solve for $x$ : $\frac{{x}^{}}{{x}^{}}17^{\left(\frac{1}{2}\right)}$ $17^{\left(\frac{1}{2}\right)}$

Solve for $x$ : $x^{\left(\frac{1}{2}\right)}=9$

Simplify: $\frac{x}{\sqrt{x}}$

Simplify: $\frac{{x}^{}+\sqrt{x}}{{x}^{}+\frac{1}{\sqrt{x}}}$

Multiply the top and bottom by $x^{\left(\frac{1}{2}\right)}$ .

Now…remember inverse functions? You find them by switching the $x$ and the $y$ and then solving for $y$ . Find the inverse of each of the following functions. To do this, in some cases, you will have to rewrite the things. For instance, in #9, you will start by writing $y=x^{\left(\frac{1}{2}\right)}$ . Switch the $x$ and the $y$ , and you get $x=y^{\left(\frac{1}{2}\right)}$ . Now what? Well, remember what that means: it means $x=\sqrt{y}$ . Once you’ve done that, you can solve for $y$ , right?

$x^{3}$

• Find the inverse function.
• Test it.

$x^{-2}$

• Find the inverse function.
• Test it.

$x^{0}$

• Find the inverse function.
• Test it.

Can you find a generalization about the inverse function of an exponent?

Graph $y=2^{x}$ by plotting points. Make sure to include both positive and negative $x$ values.

Graph $y=22^{x}$ by doubling all the y-values in the graph of $y=2^{x}$ .

Graph $y=2^{x}+1$ by taking the graph $y=2^{x}$ and “shifting” it to the left by one.

Graph $y=\left(\frac{1}{2}\right)^{x}$ by plotting points. Make sure to include both positive and negative $x$ values.

#### Questions & Answers

are nano particles real
Missy Reply
yeah
Joseph
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
Lale Reply
no can't
Lohitha
where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
has a lot of application modern world
Kamaluddeen
yes
narayan
what is variations in raman spectra for nanomaterials
Jyoti Reply
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
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
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
Brian Reply
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?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
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
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
Bob Reply
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?
Damian Reply
what king of growth are you checking .?
Renato
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Source:  OpenStax, Advanced algebra ii: activities and homework. OpenStax CNX. Sep 15, 2009 Download for free at http://cnx.org/content/col10686/1.5
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