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

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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 = amn = 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