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# Laws of Exponents PowerPoint PPT Presentation

Laws of Exponents. 7-2 through 7-4. What we call expanded notation. What we call expanded notation. What we call expanded notation. Putting it all together…. Putting it all together… =3  3  3  3  3  3. Putting it all together… =3  3  3  3  3  3

Laws of Exponents

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## Laws of Exponents

7-2 through 7-4

• What we call expanded notation

• What we call expanded notation

• What we call expanded notation

• Putting it all together…

• Putting it all together…

• =3 3 3 3 33

• Putting it all together…

• =3 3 3 3 33

• All told, how many 3’s?

• 6, so our final answer, in exponential notation, is…

• =3 3 3 3 33

• All told, how many 3’s?

• 6, so our final answer, in exponential notation, is…

• =

• All told, how many 3’s?

• Is there a quicker way?

• =

• All told, how many 3’s?

• Is there a quicker way?

• =

• All told, how many 3’s?

Absolutely; we can gain the same answer by

• Is there a quicker way?

• =

• All told, how many 3’s?

### Giving us our 1st law:

• Is there a quicker way?

• =

• All told, how many 3’s?

### Giving us our 1st law:

-When we multiply powers with the same base, we add their individual exponents.

### Make sure to differentiate between…

Exponents and Coefficients

### Make sure to differentiate between…

Exponents and Coefficients

Students will often get mixed up and apply the wrong operation to the problem.

4(9) = 36

4(9) = 36

4(9) = 36

4(9) = 36

=

=

=

6(9) = 54

=

6(9) = 54

### First steps into…

Scientific Notation!!!

1 < |a| < 10

1 < |a| < 10

n is an integer.

256,000

0.0041

256,000

0.0041

256,000

0.0041

### Keep in mind:

• a is negative when the original number is negative.

### Keep in mind:

• a is negative when the original number is negative.

• With small decimals, the absolute value of the exponent is equal to the # of zeroes, if you include a lead zero before the decimal place.

### Real world application:

• At 20 Celsius, one of water has a mass of about 9.98  grams.

### Real world application:

• At 20 Celsius, one of water has a mass of about 9.98  grams. Each gram of water contains about 3.34  molecules of water

### Real world application:

• At 20 Celsius, one of water has a mass of about 9.98  grams. Each gram of water contains about 3.34  molecules of water. How many molecules of water are contained in a swimming pool containing 200 of water?

O =

O =

O =

O =

O =

O =

O =

POWER LAW!!!

### Next Law

POWER LAW!!!

Raising an exponent inside parentheses to another exponent.

POWER LAW!!!

Example:

POWER LAW!!!

Example:

POWER LAW!!!

Example:

POWER LAW!!!

Example: =

Example: =

Example: =

### Expanded!

Which I can obtain much faster by…

Example: =

### Multiplication

Which I can obtain much faster by…

Example: =

### Power Law:

When raising an exponent to another exponent, we multiply the individual exponents

=

=

=

=

=

### Gentle reminder…

Coefficients are raised to the exponent

### Application:

Raising a product to a power

### Application:

Raising a product to a power

=

=

=

=

### Real world…

• The expression gives the kinetic energy, in joules, of an object of mass of m kg traveling at a speed of v meters per second.

### Real world…

• What is the kinetic energy of an experimental unmanned jet with a mass of kg traveling at a speed of about m/s?

=

=

=

=

=

½ (

=

½ (

joules

### Last Law…

• Moving in the opposite direction

### Again, with expanded notation:

What are a great deal of the 4’s going to do to each other?

### Cancel Out!

What are a great deal of the 4’s going to do to each other?

### Cancel Out!

What are a great deal of the 4’s going to do to each other?

### Cancel Out!

What are we left with?

### Cancel Out!

What are we left with?

### Cancel Out!

What are we left with?

Which is equivalent to…

### Cancel Out!

What are we left with?

Which is equivalent to…

### What’s the “magic” math way of turn 5 and 3 into 2?

What are we left with?

Which is equivalent to…

### Division!!!

What are we left with?

Which is equivalent to…

### Division Property of Exponents…

When dividing powers with the same base, we subtract their exponents.

ONE RESTRICTION:

### Division Property of Exponents…

ONE RESTRICTION: a  0

### Does everyone know why?

ONE RESTRICTION: a  0

### Quick hits

• When the larger exponent is in the denominator,

• When the larger exponent is in the denominator,

you can subtract

the top from the

bottom and put

### Does anyone need to see an example?

• When the larger exponent is in the denominator,

you can subtract

the top from the

bottom and put

### Scientific Notation & Population Density

Population Density is defined as:

### Scientific Notation & Population Density

Population Density is defined as:

### Example

• If the country of Wazup has a population of 3.5 • and a land size of 7 •,what is its population density?

### Example

• If the country of Wazup has a population of 3.5 • and a land size of 7 •,what is its population density?

### Last Application

• Raising an exponent to a power:

### Last Application

• Raising an exponent to a power:

• b  0

### Last Application

• When raising a fraction to an exponent

### Last Application

• When raising a fraction to an exponent

raise both the numerator and denominator to the exponent.

### Choices, choices…

• Simplify the following expression: