PRECALCULUS NYOS CHARTER SCHOOL QUARTER 3 “THE ESSENCE OF MATHEMATICS IS NOT TO MAKE SIMPLE THINGS...

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PRECALCULUS NYOS CHARTER SCHOOL QUARTER 3 “THE ESSENCE OF MATHEMATICS IS NOT TO MAKE SIMPLE THINGS COMPLICATED, BUT TO MAKE COMPLICATED THINGS SIMPLE.” ~S. GUDDER Exponents

Transcript of PRECALCULUS NYOS CHARTER SCHOOL QUARTER 3 “THE ESSENCE OF MATHEMATICS IS NOT TO MAKE SIMPLE THINGS...

Page 1: PRECALCULUS NYOS CHARTER SCHOOL QUARTER 3 “THE ESSENCE OF MATHEMATICS IS NOT TO MAKE SIMPLE THINGS COMPLICATED, BUT TO MAKE COMPLICATED THINGS SIMPLE.”

PRECALCULUSNYOS CHARTER SCHOOLQUARTER 3

“THE ESSENCE OF MATHEMATICS IS NOT TO MAKE SIMPLE THINGS COMPLICATED, BUT TO MAKE COMPLICATED THINGS SIMPLE.”  ~S. GUDDER

Exponents

Page 2: PRECALCULUS NYOS CHARTER SCHOOL QUARTER 3 “THE ESSENCE OF MATHEMATICS IS NOT TO MAKE SIMPLE THINGS COMPLICATED, BUT TO MAKE COMPLICATED THINGS SIMPLE.”

Exponents

A number is written in scientific notation when it is in the form

a * 10n

where 1 ≤ a < 10

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Exponents

Example: Write 152,000,000 in scientific notation.

Page 4: PRECALCULUS NYOS CHARTER SCHOOL QUARTER 3 “THE ESSENCE OF MATHEMATICS IS NOT TO MAKE SIMPLE THINGS COMPLICATED, BUT TO MAKE COMPLICATED THINGS SIMPLE.”

Exponents

Example: Write 152,000,000 in scientific notation.

= 1.52 * 108

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Exponents

Example: Write 0.0000000068 in scientific notation.

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Exponents

Example: Write 0.0000000068 in scientific notation.

= 6.8 * 10 -9

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Exponents

Property Definition Example

Product aman = am+n 5357 = 510

Power of a Power

Power of a Quotient

Power of a Product

Quotient

Page 8: PRECALCULUS NYOS CHARTER SCHOOL QUARTER 3 “THE ESSENCE OF MATHEMATICS IS NOT TO MAKE SIMPLE THINGS COMPLICATED, BUT TO MAKE COMPLICATED THINGS SIMPLE.”

Exponents

Property Definition Example

Product aman = am+n 5357 = 510

Power of a Power

(am)n = amn (25)4 = 220

Power of a Quotient

Power of a Product

Quotient

Page 9: PRECALCULUS NYOS CHARTER SCHOOL QUARTER 3 “THE ESSENCE OF MATHEMATICS IS NOT TO MAKE SIMPLE THINGS COMPLICATED, BUT TO MAKE COMPLICATED THINGS SIMPLE.”

Exponents

Property Definition Example

Product aman = am+n 5357 = 510

Power of a Power

(am)n = amn (25)4 = 220

Power of a Quotient

Power of a Product

Quotient

Page 10: PRECALCULUS NYOS CHARTER SCHOOL QUARTER 3 “THE ESSENCE OF MATHEMATICS IS NOT TO MAKE SIMPLE THINGS COMPLICATED, BUT TO MAKE COMPLICATED THINGS SIMPLE.”

Exponents

Property Definition Example

Product aman = am+n 5357 = 510

Power of a Power

(am)n = amn (25)4 = 220

Power of a Quotient

Power of a Product

(ab)m = ambm (2x)3 = 23x3 = 8x3

Quotient

Page 11: PRECALCULUS NYOS CHARTER SCHOOL QUARTER 3 “THE ESSENCE OF MATHEMATICS IS NOT TO MAKE SIMPLE THINGS COMPLICATED, BUT TO MAKE COMPLICATED THINGS SIMPLE.”

Exponents

Property Definition Example

Product aman = am+n 5357 = 510

Power of a Power

(am)n = amn (25)4 = 220

Power of a Quotient

Power of a Product

(ab)m = ambm (2x)3 = 23x3 = 8x3

Quotient = am-n = 52 = 25

Page 12: PRECALCULUS NYOS CHARTER SCHOOL QUARTER 3 “THE ESSENCE OF MATHEMATICS IS NOT TO MAKE SIMPLE THINGS COMPLICATED, BUT TO MAKE COMPLICATED THINGS SIMPLE.”

Exponents

Example: Evaluate.

Page 13: PRECALCULUS NYOS CHARTER SCHOOL QUARTER 3 “THE ESSENCE OF MATHEMATICS IS NOT TO MAKE SIMPLE THINGS COMPLICATED, BUT TO MAKE COMPLICATED THINGS SIMPLE.”

Exponents

Example: Evaluate.

=

= 27

= 128

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Exponents

Example: Simplify.

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Exponents

Example: Simplify.

=

=

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Exponents

is the same as

Page 17: PRECALCULUS NYOS CHARTER SCHOOL QUARTER 3 “THE ESSENCE OF MATHEMATICS IS NOT TO MAKE SIMPLE THINGS COMPLICATED, BUT TO MAKE COMPLICATED THINGS SIMPLE.”

Exponents

is the same as

is the same as

is the same as

is the same as 11

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Exponents

Example: Evaluate.

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Exponents

Example: Evaluate.

=

=

= 5

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Exponents

Example: Evaluate.

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Exponents

Example: Evaluate.

=

= 2

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Exponents

Example: Simplify.

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Exponents

Example: Simplify.

=

=

= 3c

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Exponents

Example: Simplify.

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Exponents

Example: Simplify.

= =

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Exponents

Example: Simplify.

= = = = =

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Exponents

is the same as

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Exponents

is the same as

is the same as

is the same as

iff is a real number

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Exponents

Example: Evaluate.

Page 30: PRECALCULUS NYOS CHARTER SCHOOL QUARTER 3 “THE ESSENCE OF MATHEMATICS IS NOT TO MAKE SIMPLE THINGS COMPLICATED, BUT TO MAKE COMPLICATED THINGS SIMPLE.”

Exponents

Example: Evaluate.

=

= 53

= 125

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Exponents

Example: Evaluate.

Page 32: PRECALCULUS NYOS CHARTER SCHOOL QUARTER 3 “THE ESSENCE OF MATHEMATICS IS NOT TO MAKE SIMPLE THINGS COMPLICATED, BUT TO MAKE COMPLICATED THINGS SIMPLE.”

Exponents

Example: Evaluate.

=

=

= 4

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Exponents

Example: Simplify.

Page 34: PRECALCULUS NYOS CHARTER SCHOOL QUARTER 3 “THE ESSENCE OF MATHEMATICS IS NOT TO MAKE SIMPLE THINGS COMPLICATED, BUT TO MAKE COMPLICATED THINGS SIMPLE.”

Exponents

Example: Simplify.

=

=

=

Page 35: PRECALCULUS NYOS CHARTER SCHOOL QUARTER 3 “THE ESSENCE OF MATHEMATICS IS NOT TO MAKE SIMPLE THINGS COMPLICATED, BUT TO MAKE COMPLICATED THINGS SIMPLE.”

Exponents

How do we know when to use absolute value bars?

Variable Taken Out from Even Index Odd Exponent

Page 36: PRECALCULUS NYOS CHARTER SCHOOL QUARTER 3 “THE ESSENCE OF MATHEMATICS IS NOT TO MAKE SIMPLE THINGS COMPLICATED, BUT TO MAKE COMPLICATED THINGS SIMPLE.”

Exponents

Example: Simplify.

Page 37: PRECALCULUS NYOS CHARTER SCHOOL QUARTER 3 “THE ESSENCE OF MATHEMATICS IS NOT TO MAKE SIMPLE THINGS COMPLICATED, BUT TO MAKE COMPLICATED THINGS SIMPLE.”

Exponents

Example: Simplify.

=

=

=

Page 38: PRECALCULUS NYOS CHARTER SCHOOL QUARTER 3 “THE ESSENCE OF MATHEMATICS IS NOT TO MAKE SIMPLE THINGS COMPLICATED, BUT TO MAKE COMPLICATED THINGS SIMPLE.”

Exponents

Example: Simplify.

Page 39: PRECALCULUS NYOS CHARTER SCHOOL QUARTER 3 “THE ESSENCE OF MATHEMATICS IS NOT TO MAKE SIMPLE THINGS COMPLICATED, BUT TO MAKE COMPLICATED THINGS SIMPLE.”

Exponents

Example: Simplify.

=

=

=

=

Page 40: PRECALCULUS NYOS CHARTER SCHOOL QUARTER 3 “THE ESSENCE OF MATHEMATICS IS NOT TO MAKE SIMPLE THINGS COMPLICATED, BUT TO MAKE COMPLICATED THINGS SIMPLE.”

Exponents

Example: Solve. 16 =

Page 41: PRECALCULUS NYOS CHARTER SCHOOL QUARTER 3 “THE ESSENCE OF MATHEMATICS IS NOT TO MAKE SIMPLE THINGS COMPLICATED, BUT TO MAKE COMPLICATED THINGS SIMPLE.”

Exponents

Example: Solve. 16 =

= x

= x

32 = x

Page 42: PRECALCULUS NYOS CHARTER SCHOOL QUARTER 3 “THE ESSENCE OF MATHEMATICS IS NOT TO MAKE SIMPLE THINGS COMPLICATED, BUT TO MAKE COMPLICATED THINGS SIMPLE.”

Exponents

Example: Solve. 734 = + 5

Page 43: PRECALCULUS NYOS CHARTER SCHOOL QUARTER 3 “THE ESSENCE OF MATHEMATICS IS NOT TO MAKE SIMPLE THINGS COMPLICATED, BUT TO MAKE COMPLICATED THINGS SIMPLE.”

Exponents

Example: Solve. 734 = + 5

729 =

= x

6,561 = x