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- 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.
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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
If c is the cost function for a particular product, find the marginal cost functions and their
values at x=10 a. c(x) = 800+ 0.04x + 0.0002x² b. c(x) = 250 + 100x + 0.001x²
how can I find set theory
how can I find set theory
Jarvis
is there an error on the one about the dime's thickness? says 2.2x10⁶=0.00135 m
hi, interested in algebra
how to reduce an equation?
Makan
by manipulation of both side
Al
9(y+8)-27 is 9y+45.
Why can't you reduce that to y+5? I know that's wrong but can't explain why
when you reduce an equation to its simplest terms, you can't change the value of the equation. reducing it to y + 5 is equivalent to dividing it by 9 which changes the value. you can multiply it by 1 or 9/9 which would give 9(y + 5). multiplying it by one does not change the value.
Philip
Given a polynomial expression, factor out the greatest common factor.
WHAT IS QUADRATIC EQUATION?
WHAT IS SYSTEM OF LINEAR INEWUALITIES?
Charles
WHAT IS SYSTEM OF LINEAR INEWUALITIES?
Charles
what are equations?
Charles
Definition of economics according to
karl Marx
Thomas malthus
Jeremy bentham
David Ricardo
J.K
Rakiya
Please help me is assignment
Rakiya
The 47th problem of Euclid
Kenneth
show that the set of all natural number form semi group under the composition of addition
what is the meaning
Dominic
explain and give four Example hyperbolic function
The denominator of a certain fraction is 9 more than the numerator. If 6 is added to both terms of the
fraction, the value of the fraction becomes 2/3. Find the original fraction.
2. The sum of the least and greatest of 3 consecutive integers is 60. What are the valu
1. x + 6 2
-------------- = _
x + 9 + 6 3
x + 6 3
----------- x -- (cross multiply)
x + 15 2
3(x + 6) = 2(x + 15)
3x + 18 = 2x + 30 (-2x from both)
x + 18 = 30 (-18 from both)
x = 12
Test:
12 + 6 18 2
-------------- = --- = ---
12 + 9 + 6 27 3
Pawel
2.
(x) + (x + 2) = 60
2x + 2 = 60
2x = 58
x = 29
29, 30, & 31
Pawel
on number 2 question How did you got 2x +2
Ifeanyi
combine like terms. x + x + 2 is same as 2x + 2
Pawel
Q2
x+(x+2)+(x+4)=60
3x+6=60
3x+6-6=60-6
3x=54
3x/3=54/3
x=18
:. The numbers are 18,20 and 22
Naagmenkoma
Mark and Don are planning to sell each of their marble collections at a garage sale. If Don has 1 more than 3 times the number of marbles Mark has, how many does each boy have to sell if the total number of marbles is 113?
Mark = x,. Don = 3x + 1
x + 3x + 1 = 113
4x = 112, x = 28
Mark = 28, Don = 85, 28 + 85 = 113
Pawel
how do I set up the problem?
what is a solution set?
Harshika
find the subring of gaussian integers?
Rofiqul
hello, I am happy to help!
please can go further on polynomials quadratic
Abdullahi
I need quadratic equation link to Alpa Beta
Source:
OpenStax, College algebra. OpenStax CNX. Feb 06, 2015 Download for free at https://legacy.cnx.org/content/col11759/1.3
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