Algebra 2 Ch 2.1 Use Properties of Exponents.notebook
Algebra 2 Ch 2.1 Use Properties of Exponents.notebook
Use Properties of Exponents
August 30, 2012
Use Properties of Exponents
Product Rule Learning Objecves for CH2.1: Properes of Exponents • 7 Properes of Exponents • Scienfic Notaon
Jun 233:15 PM
Use Properties of Exponents
Power to a Power Rule
Example
Jun 233:15 PM
Use Properties of Exponents Negative Exponent Rule
Example:
Jun 233:15 PM
Example:
Jun 233:15 PM
Use Properties of Exponents
Power of a Product Rule
Example:
Jun 233:15 PM
Use Properties of Exponents Zero Exponent Rule
Examples
Jun 233:15 PM
1
Algebra 2 Ch 2.1 Use Properties of Exponents.notebook
Use Properties of Exponents
August 30, 2012
Use Properties of Exponents
Quotient Rule
Example:
Jun 233:15 PM
Use Properties of Exponents
Jun 233:15 PM
Use Properties of Exponents
Jun 233:15 PM
Jun 233:15 PM
Use Properties of Exponents
Jun 233:15 PM
Use Properties of Exponents
Jun 233:15 PM
2
Algebra 2 Ch 2.1 Use Properties of Exponents.notebook
Use Properties of Exponents
August 30, 2012
Use Properties of Exponents There are too many ways that Properties of Exponents can be used to show an example of every way. • Go slowly. • Examine all possibilities. • Do not quit.
Jun 233:15 PM
Use Properties of Exponents Scientific Notation Scientific notation allows us to write very big or very small numbers in manner that is easy to read. When a number is written in scientific notation, it is made up of two parts. The left hand part is a number that is greater than or equal to one, but less than ten, and the right hand part is ten raised to a power. This power may be positive or negative. When the power is positive, the original number is greater than 1, and when the power is negative, the original number is less than one. For example, when we write 50,000 in scientific notation, it is written as 5 x 104. When we write .00008 in scientific notation, it is written as 8 x 105 .
Jun 233:15 PM
Use Properties of Exponents Small Numbers For a small number such as 0.000005 we will be moving the decimal point to the right so that we have a number greater than or equal to one, but less than ten. The decimal point is moved 6 places to the right and this too is going to be the power we use with 10, and we have found a number between 1 and 10 and that number is 5. However when we move a decimal point to the right, the exponent will be negative. Since we have found our number between 1 and 10 and our power, we can now write 0.000005 in scientific notation as: 5 x 10 6 If we have a number such as 0.0000739 we use the same process. The decimal point is moved to the right until we get a number that is between 1 and 10. When we move our decimal point 5 places to the right, we get 7.39 and our power will be 5. So 0.0000739 becomes 7.39 x 10 5.
Jun 233:15 PM
Jun 233:15 PM
Use Properties of Exponents Big Numbers For a large number such as 900,000 we will be moving the decimal point to the left so that we have a number greater than or equal to one, but less than ten. The decimal point is moved 5 places to the left, and this is an important number to remember, because this is going to be the power we use with 10. Since we now have found that 9 is our number between 1 and 10 and our power which is 5, we can now write 900,000 in scientific notation as: 9 x 10 5 If we have a number such as 456,000,000 we use the same
process. The decimal point is moved to the left until we get a number that is between 1 and 10. When we move our decimal point 8 places to the left, we get 4.56 and our power will be 8. So 456,000,000 becomes 4.56 x 10 8.
Jun 233:15 PM
Use Properties of Exponents Moving from scientific notation to standard numbers. If you have a number written in scientific notation, you may be asked to write it as a standard number. A number such as 3.28 x 10 4 can be easily converted. All you have to do is move the decimal point to the right the number of spaces that is the same as the power that 10 is raised to. So for this number, you move your decimal point 4 spaces to the right, and you number is 32,800. The process is very similar when you have negative exponents. For 9.49 x 10 5 you move the decimal point 5 places to the left, and your number is 0.0000949
Jun 233:15 PM
3
Algebra 2 Ch 2.1 Use Properties of Exponents.notebook
August 30, 2012
Use Properties of Exponents Learning Objecves for CH2.1: Properes of Exponents • 7 Properes of Exponents • Scienfic Notaon
Jun 233:15 PM
4
Use Properties of Exponents
August 30, 2012
Use Properties of Exponents
Product Rule Learning Objecves for CH2.1: Properes of Exponents • 7 Properes of Exponents • Scienfic Notaon
Jun 233:15 PM
Use Properties of Exponents
Power to a Power Rule
Example
Jun 233:15 PM
Use Properties of Exponents Negative Exponent Rule
Example:
Jun 233:15 PM
Example:
Jun 233:15 PM
Use Properties of Exponents
Power of a Product Rule
Example:
Jun 233:15 PM
Use Properties of Exponents Zero Exponent Rule
Examples
Jun 233:15 PM
1
Algebra 2 Ch 2.1 Use Properties of Exponents.notebook
Use Properties of Exponents
August 30, 2012
Use Properties of Exponents
Quotient Rule
Example:
Jun 233:15 PM
Use Properties of Exponents
Jun 233:15 PM
Use Properties of Exponents
Jun 233:15 PM
Jun 233:15 PM
Use Properties of Exponents
Jun 233:15 PM
Use Properties of Exponents
Jun 233:15 PM
2
Algebra 2 Ch 2.1 Use Properties of Exponents.notebook
Use Properties of Exponents
August 30, 2012
Use Properties of Exponents There are too many ways that Properties of Exponents can be used to show an example of every way. • Go slowly. • Examine all possibilities. • Do not quit.
Jun 233:15 PM
Use Properties of Exponents Scientific Notation Scientific notation allows us to write very big or very small numbers in manner that is easy to read. When a number is written in scientific notation, it is made up of two parts. The left hand part is a number that is greater than or equal to one, but less than ten, and the right hand part is ten raised to a power. This power may be positive or negative. When the power is positive, the original number is greater than 1, and when the power is negative, the original number is less than one. For example, when we write 50,000 in scientific notation, it is written as 5 x 104. When we write .00008 in scientific notation, it is written as 8 x 105 .
Jun 233:15 PM
Use Properties of Exponents Small Numbers For a small number such as 0.000005 we will be moving the decimal point to the right so that we have a number greater than or equal to one, but less than ten. The decimal point is moved 6 places to the right and this too is going to be the power we use with 10, and we have found a number between 1 and 10 and that number is 5. However when we move a decimal point to the right, the exponent will be negative. Since we have found our number between 1 and 10 and our power, we can now write 0.000005 in scientific notation as: 5 x 10 6 If we have a number such as 0.0000739 we use the same process. The decimal point is moved to the right until we get a number that is between 1 and 10. When we move our decimal point 5 places to the right, we get 7.39 and our power will be 5. So 0.0000739 becomes 7.39 x 10 5.
Jun 233:15 PM
Jun 233:15 PM
Use Properties of Exponents Big Numbers For a large number such as 900,000 we will be moving the decimal point to the left so that we have a number greater than or equal to one, but less than ten. The decimal point is moved 5 places to the left, and this is an important number to remember, because this is going to be the power we use with 10. Since we now have found that 9 is our number between 1 and 10 and our power which is 5, we can now write 900,000 in scientific notation as: 9 x 10 5 If we have a number such as 456,000,000 we use the same
process. The decimal point is moved to the left until we get a number that is between 1 and 10. When we move our decimal point 8 places to the left, we get 4.56 and our power will be 8. So 456,000,000 becomes 4.56 x 10 8.
Jun 233:15 PM
Use Properties of Exponents Moving from scientific notation to standard numbers. If you have a number written in scientific notation, you may be asked to write it as a standard number. A number such as 3.28 x 10 4 can be easily converted. All you have to do is move the decimal point to the right the number of spaces that is the same as the power that 10 is raised to. So for this number, you move your decimal point 4 spaces to the right, and you number is 32,800. The process is very similar when you have negative exponents. For 9.49 x 10 5 you move the decimal point 5 places to the left, and your number is 0.0000949
Jun 233:15 PM
3
Algebra 2 Ch 2.1 Use Properties of Exponents.notebook
August 30, 2012
Use Properties of Exponents Learning Objecves for CH2.1: Properes of Exponents • 7 Properes of Exponents • Scienfic Notaon
Jun 233:15 PM
4
