# Elementary kws006/Precalculus/1.0_Algebra_Review... Exponential Notation About three centuries ago,

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### Transcript of Elementary kws006/Precalculus/1.0_Algebra_Review... Exponential Notation About three centuries ago,

Elementary Functions Part 1, Functions

Lecture 1.0a, Excellence in Algebra: Exponents

Dr. Ken W. Smith

Sam Houston State University

2013

Smith (SHSU) Elementary Functions 2013 1 / 17

Excellence in Algebra

Before we can be successful in science and calculus, we need some comfort with algebra. Here are two major algebra computations we do throughout this class (and you will do throughout your career!)

exponential notation, and

polynomial arithmetic

Here we review exponential notation.

Smith (SHSU) Elementary Functions 2013 2 / 17

Excellence in Algebra

Before we can be successful in science and calculus, we need some comfort with algebra. Here are two major algebra computations we do throughout this class (and you will do throughout your career!)

exponential notation, and

polynomial arithmetic

Here we review exponential notation.

Smith (SHSU) Elementary Functions 2013 2 / 17

Excellence in Algebra

Before we can be successful in science and calculus, we need some comfort with algebra. Here are two major algebra computations we do throughout this class (and you will do throughout your career!)

exponential notation, and

polynomial arithmetic

Here we review exponential notation.

Smith (SHSU) Elementary Functions 2013 2 / 17

Excellence in Algebra

exponential notation, and

polynomial arithmetic

Here we review exponential notation.

Smith (SHSU) Elementary Functions 2013 2 / 17

Excellence in Algebra

exponential notation, and

polynomial arithmetic

Here we review exponential notation.

Smith (SHSU) Elementary Functions 2013 2 / 17

Excellence in Algebra

exponential notation, and

polynomial arithmetic

Here we review exponential notation.

Smith (SHSU) Elementary Functions 2013 2 / 17

Exponential Notation

About three centuries ago, scientists developed abbreviations for multiplication of a variable, replacing

x · x by x2, x · x · x by x3 and x · x · x · x · x by x5, etc.

This is just an abbreviation! The exponent merely counts the number of times the base appears in the product.

This leads to some basic “rules” consistent with the abbreviation.

For example, x3 · x2 = (x · x · x) · (x · x) = x5 So if we multiply objects with the same base (x) we should add the exponents:

Similarly, x3

x2 =

x · x · x x · x

= x

1

x

x

x

x = x

When we divide objects with the same base (x) we subtract the exponents.

(x3)2 = (x · x · x)2 = (x · x · x)(x · x · x) = x · x · x · x · x · x = x6. Repeated exponentiation leads to multiplying exponents.

Smith (SHSU) Elementary Functions 2013 3 / 17

Exponential Notation

About three centuries ago, scientists developed abbreviations for multiplication of a variable, replacing

x · x by x2, x · x · x by x3 and x · x · x · x · x by x5, etc.

This is just an abbreviation! The exponent merely counts the number of times the base appears in the product.

This leads to some basic “rules” consistent with the abbreviation.

For example, x3 · x2 = (x · x · x) · (x · x) = x5 So if we multiply objects with the same base (x) we should add the exponents:

Similarly, x3

x2 =

x · x · x x · x

= x

1

x

x

x

x = x

When we divide objects with the same base (x) we subtract the exponents.

(x3)2 = (x · x · x)2 = (x · x · x)(x · x · x) = x · x · x · x · x · x = x6. Repeated exponentiation leads to multiplying exponents.

Smith (SHSU) Elementary Functions 2013 3 / 17

Exponential Notation

About three centuries ago, scientists developed abbreviations for multiplication of a variable, replacing

x · x by x2, x · x · x by x3 and x · x · x · x · x by x5, etc.

This is just an abbreviation! The exponent merely counts the number of times the base appears in the product.

This leads to some basic “rules” consistent with the abbreviation.

For example, x3 · x2 = (x · x · x) · (x · x) = x5 So if we multiply objects with the same base (x) we should add the exponents:

Similarly, x3

x2 =

x · x · x x · x

= x

1

x

x

x

x = x

When we divide objects with the same base (x) we subtract the exponents.

(x3)2 = (x · x · x)2 = (x · x · x)(x · x · x) = x · x · x · x · x · x = x6. Repeated exponentiation leads to multiplying exponents.

Smith (SHSU) Elementary Functions 2013 3 / 17

Exponential Notation

x · x by x2, x · x · x by x3 and x · x · x · x · x by x5, etc.

This leads to some basic “rules” consistent with the abbreviation.

Similarly, x3

x2 =

x · x · x x · x

= x

1

x

x

x

x = x

When we divide objects with the same base (x) we subtract the exponents.

Smith (SHSU) Elementary Functions 2013 3 / 17

Exponential Notation

x · x by x2, x · x · x by x3 and x · x · x · x · x by x5, etc.

This leads to some basic “rules” consistent with the abbreviation.

Similarly, x3

x2 =

x · x · x x · x

= x

1

x

x

x

x = x

When we divide objects with the same base (x) we subtract the exponents.

Smith (SHSU) Elementary Functions 2013 3 / 17

Exponential Notation

x · x by x2, x · x · x by x3 and x · x · x · x · x by x5, etc.

This leads to some basic “rules” consistent with the abbreviation.

Similarly, x3

x2 =

x · x · x x · x

= x

1

x

x

x

x = x

When we divide objects with the same base (x) we subtract the exponents.

Smith (SHSU) Elementary Functions 2013 3 / 17

Exponential Notation

x · x by x2, x · x · x by x3 and x · x · x · x · x by x5, etc.

This leads to some basic “rules” consistent with the abbreviation.

Similarly, x3

x2 =

x · x · x x · x

= x

1

x

x

x

x = x

When we divide objects with the same base (x) we subtract the exponents.

Smith (SHSU) Elementary Functions 2013 3 / 17

Exponential Notation

x · x by x2, x · x · x by x3 and x · x · x · x · x by x5, etc.

This is just an abbreviation! The exponent merely counts the number of times th

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