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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...

PRECALCULUSNYOS CHARTER SCHOOLQUARTER 3

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

Exponents

Exponents

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

a * 10n

where 1 ≤ a < 10

Exponents

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

Exponents

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

= 1.52 * 108

Exponents

Example: Write 0.0000000068 in scientific notation.

Exponents

Example: Write 0.0000000068 in scientific notation.

= 6.8 * 10 -9

Exponents

Property Definition Example

Product aman = am+n 5357 = 510

Power of a Power

Power of a Quotient

Power of a Product

Quotient

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

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

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

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

Exponents

Example: Evaluate.

Exponents

Example: Evaluate.

=

= 27

= 128

Exponents

Example: Simplify.

Exponents

Example: Simplify.

=

=

Exponents

is the same as

Exponents

is the same as

is the same as

is the same as

is the same as 11

Exponents

Example: Evaluate.

Exponents

Example: Evaluate.

=

=

= 5

Exponents

Example: Evaluate.

Exponents

Example: Evaluate.

=

= 2

Exponents

Example: Simplify.

Exponents

Example: Simplify.

=

=

= 3c

Exponents

Example: Simplify.

Exponents

Example: Simplify.

= =

Exponents

Example: Simplify.

= = = = =

Exponents

is the same as

Exponents

is the same as

is the same as

is the same as

iff is a real number

Exponents

Example: Evaluate.

Exponents

Example: Evaluate.

=

= 53

= 125

Exponents

Example: Evaluate.

Exponents

Example: Evaluate.

=

=

= 4

Exponents

Example: Simplify.

Exponents

Example: Simplify.

=

=

=

Exponents

How do we know when to use absolute value bars?

Variable Taken Out from Even Index Odd Exponent

Exponents

Example: Simplify.

Exponents

Example: Simplify.

=

=

=

Exponents

Example: Simplify.

Exponents

Example: Simplify.

=

=

=

=

Exponents

Example: Solve. 16 =

Exponents

Example: Solve. 16 =

= x

= x

32 = x

Exponents

Example: Solve. 734 = + 5

Exponents

Example: Solve. 734 = + 5

729 =

= x

6,561 = x