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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…
- =3 3 3 3 33

- Putting it all together…
- =3 3 3 3 33
- All told, how many 3’s?

- 6, so our final answer, in exponential notation, is…
- =3 3 3 3 33
- 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?
Absolutely; we can gain the same answer by adding exponents.

Giving us our 1st law:

- Is there a quicker way?
- =
- All told, how many 3’s?
Absolutely; we can gain the same answer by adding exponents.

Giving us our 1st law:

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.

Example of what I mean…

4(9) = 36

Example of what I mean…

4(9) = 36

Example of what I mean…

4(9) = 36

Example of what I mean…

4(9) = 36

First steps into…

Scientific Notation!!!

First steps into…

1 < |a| < 10

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?

Next Law

POWER LAW!!!

Power Law:

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

Power Law 1st:

Power Law 1st:

Power Law 1st:

Gentle reminder…

Coefficients are raised to the exponent

Application:

Raising a product to a power

Application:

Raising a product to a power

Life lesson: handle negatives at the end of the problem.

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?

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?

Division Property of Exponents…

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

Division Property of Exponents…

ONE RESTRICTION:

Division Property of Exponents…

ONE RESTRICTION: a 0

Does everyone know why?

ONE RESTRICTION: a 0

Helpful Hint: Saving Time

- When the larger exponent is in the denominator,

Helpful Hint: Saving Time

- When the larger exponent is in the denominator,
you can subtract

the top from the

bottom and put

your answer in the denominator

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

your answer in the denominator

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:

Last Application

- 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:

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