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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 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.

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

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

Exponents and Coefficients

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

Scientific Notation!!!

1 < |a| < 10

1 < |a| < 10

n is an integer.

256,000

0.0041

256,000

0.0041

256,000

0.0041

- a is negative when the original number is negative.

- 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.

- At 20 Celsius, one of water has a mass of about 9.98 grams.

- 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

- 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!!!

POWER LAW!!!

Raising an exponent inside parentheses to another exponent.

POWER LAW!!!

Example:

POWER LAW!!!

Example:

POWER LAW!!!

Example:

POWER LAW!!!

Example: =

Return to the product law

Example: =

Return to the product law

Example: =

Which I can obtain much faster by…

Example: =

Which I can obtain much faster by…

Example: =

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

=

=

=

=

=

Coefficients are raised to the exponent

Raising a product to a power

Raising a product to a power

=

=

=

=

- 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.

- 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

- Moving in the opposite direction

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

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

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

What are we left with?

What are we left with?

What are we left with?

Which is equivalent to…

What are we left with?

Which is equivalent to…

What are we left with?

Which is equivalent to…

What are we left with?

Which is equivalent to…

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

ONE RESTRICTION:

ONE RESTRICTION: a 0

ONE RESTRICTION: a 0

- 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

your answer in the denominator

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

the top from the

bottom and put

your answer in the denominator

Population Density is defined as:

Population Density is defined as:

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

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

- Raising an exponent to a power:

- Raising an exponent to a power:

- b 0

- When raising a fraction to an exponent

- When raising a fraction to an exponent
raise both the numerator and denominator to the exponent.

- Simplify the following expression: