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- Algebra and trigonometry
- 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.
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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.
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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
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Questions & Answers
the diagram of the digestive system
allimentary cannel
Ogenrwot
They formed in two ways first when one sperm and one egg are splited by mitosis or two sperm and two eggs join together
Oluwatobi
Genetics is the study of heredity
Misack
how does twins formed?
Misack
discuss biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles
the study of living organisms and their interactions with one another and their environments
AI-Robot
the study of living organisms and their interactions with one another and their environment.
Wine
discuss the biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles in an essay form
list any five characteristics of the blood cells
Shaker
lack electricity and its more savely than electronic microscope because its naturally by using of light
advantage of electronic microscope is easily and clearly while disadvantage is dangerous because its electronic. advantage of light microscope is savely and naturally by sun while disadvantage is not easily,means its not sharp and not clear
Abdullahi
cell theory state that every organisms composed of one or more cell,cell is the basic unit of life
Abdullahi
is like gone fail us
DENG
cells is the basic structure and functions of all living things
Ramadan
is organisms that are similar into groups called tara
Yamosa
in what situation (s) would be the use of a scanning electron microscope be ideal and why?
A scanning electron microscope (SEM) is ideal for situations requiring high-resolution imaging of surfaces. It is commonly used in materials science, biology, and geology to examine the topography and composition of samples at a nanoscale level. SEM is particularly useful for studying fine details,
Hilary
cell is the building block of life.
Diversity of living thing
ISCONT
Cell division is the process by which a single cell divides into two or more daughter cells. It is a fundamental process in all living organisms and is essential for growth, development, and reproduction. Cell division can occur through either mitosis or meiosis.
AI-Robot
life is defined as any system capable of performing functions such as eating, metabolizing,excreting,breathing,moving,Growing,reproducing,and responding to external stimuli.
Mohamed
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Source:
OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
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