-
Home
- College algebra
- Prerequisites
- Exponents and scientific notation
Key equations
Rules of Exponents
For nonzero real numbers
and
and integers
and
|
Product rule |
|
Quotient rule |
|
Power rule |
|
Zero exponent rule |
|
Negative rule |
|
Power of a product rule |
|
Power of a quotient rule |
|
Key concepts
- Products of exponential expressions with the same base can be simplified by adding exponents. See
[link] .
- Quotients of exponential expressions with the same base can be simplified by subtracting exponents. See
[link] .
- Powers of exponential expressions with the same base can be simplified by multiplying exponents. See
[link] .
- An expression with exponent zero is defined as 1. See
[link] .
- An expression with a negative exponent is defined as a reciprocal. See
[link] and
[link] .
- The power of a product of factors is the same as the product of the powers of the same factors. See
[link] .
- The power of a quotient of factors is the same as the quotient of the powers of the same factors. See
[link] .
- The rules for exponential expressions can be combined to simplify more complicated expressions. See
[link] .
- Scientific notation uses powers of 10 to simplify very large or very small numbers. See
[link] and
[link] .
- Scientific notation may be used to simplify calculations with very large or very small numbers. See
[link] and
[link] .
Section exercises
Verbal
Is
the same as
Explain.
No, the two expressions are not the same. An exponent tells how many times you multiply the base. So
is the same as
which is 8.
is the same as
which is 9.
Got questions? Get instant answers now!
Numeric
For the following exercises, simplify the given expression. Write answers with positive exponents.
For the following exercises, write each expression with a single base. Do not simplify further. Write answers with positive exponents.
For the following exercises, express the decimal in scientific notation.
For the following exercises, convert each number in scientific notation to standard notation.
Algebraic
For the following exercises, simplify the given expression. Write answers with positive exponents.
Real-world applications
Technology
For the following exercises, use a graphing calculator to simplify. Round the answers to the nearest hundredth.
Extensions
For the following exercises, simplify the given expression. Write answers with positive exponents.
Avogadro’s constant is used to calculate the number of particles in a mole. A mole is a basic unit in chemistry to measure the amount of a substance. The constant is
Write Avogadro’s constant in standard notation.
Got questions? Get instant answers now!
Planck’s constant is an important unit of measure in quantum physics. It describes the relationship between energy and frequency. The constant is written as
Write Planck’s constant in standard notation.
0.000000000000000000000000000000000662606957
Got questions? Get instant answers now!
Questions & Answers
it is the relatively stable flow of income
what is circular flow of income
branches of macroeconomics
what is Flexible exchang rate?
is gdp a reliable measurement of wealth
introduction to econometrics
Why is unemployment rate never zero at full employment?
bcoz of existence of frictional unemployment in our economy.
Umashankar
what is flexible exchang rate?
poudel
due to existence of the pple with disabilities
Abdulraufu
the demand of a good rises, causing the demand for another good to fall
is it possible to leave every good at the same level
Joseph
I don't think so. because check it, if the demand for chicken increases, people will no longer consume fish like they used to causing a fall in the demand for fish
Anuolu
is not really possible to let the value of a goods to be same at the same time.....
Salome
Suppose the inflation rate is 6%, does it mean that all the goods you purchase will cost
6% more than previous year? Provide with reasoning.
Not necessarily. To measure the inflation rate economists normally use an averaged price index of a basket of certain goods. So if you purchase goods included in the basket, you will notice that you pay 6% more, otherwise not necessarily.
Waeth
discus major problems of macroeconomics
what is the problem of macroeconomics
Yoal
Economic growth
Stable prices
and low unemployment
Ephraim
explain inflationcause and itis degre
increase in general price levels
WEETO
Good day
How do I calculate this question: C= 100+5yd G= 2000 T= 2000 I(planned)=200.
Suppose the actual output is 3000. What is the level of planned expenditures at this level of output?
how to calculate actual output?
Chisomo
how to calculate the equilibrium income
Beshir
Criteria for determining money supply
who we can define macroeconomics in one line
Muhammad
Aggregate demand
Mohammed
C=k100 +9y and i=k50.calculate the equilibrium level of output
nawalparasi district
from belatari
Amisha
I am Camara from Guinea west Africa... happy to meet you guys here
Sekou
ahile becheclor ho
Amisha
hjr ktm bta ho
ani k kaam grnu hunxa tw
Amisha
money as unit of account means what?
Kalombe
A unit of account is something that can be used to value goods and services and make calculations
Jim
all of you please speak in English I can't understand you're language
Muhammad
I want to know how can we define macroeconomics in one line
Muhammad
it must be .9 or 0.9
no Mpc is greater than 1
Y=100+.9Y+50
Y-.9Y=150
0.1Y/0.1=150/0.1
Y=1500
Kalombe
Mercy is it clear?😋
Kalombe
hi can someone help me on this question
If a negative shocks shifts the IS curve to the left, what type of policy do you suggest so as to stabilize the level of output?
discuss your answer using appropriate graph.
if interest rate is increased this will will reduce the level of income shifting the curve to the left ◀️
Kalombe
Got questions? Join the online conversation and get instant answers!
Source:
OpenStax, College algebra. OpenStax CNX. Feb 06, 2015 Download for free at https://legacy.cnx.org/content/col11759/1.3
Google Play and the Google Play logo are trademarks of Google Inc.