Presentation is loading. Please wait.

Presentation is loading. Please wait.

4.1 The Product Rule and Power Rules for Exponents

Similar presentations


Presentation on theme: "4.1 The Product Rule and Power Rules for Exponents"— Presentation transcript:

1 4.1 The Product Rule and Power Rules for Exponents
Review: PEMDAS (order of operations) – note that exponentiation is number 2. Product rule for exponents: Example:

2 4.1 The Product Rule and Power Rules for Exponents
Power Rule (a) for exponents: Power Rule (b) for exponents: Power Rule (c) for exponents:

3 4.1 The Product Rule and Power Rules for Exponents
A few tricky ones:

4 4.1 The Product Rule and Power Rules for Exponents
Examples (true or false):

5 4.2 Integer Exponents and the Quotient Rule
Definition of a zero exponent: Definition of a negative exponent:

6 4.2 Integer Exponents and the Quotient Rule
Changing from negative to positive exponents: Quotient rule for exponents:

7 4.2 Integer Exponents and the Quotient Rule
Examples:

8 4.3 An Application of Exponents: Scientific Notation
Writing a number in scientific notation: Move the decimal point to the right of the first non-zero digit. Count the places you moved the decimal point. The number of places that you counted in step 2 is the exponent (without the sign) If your original number (without the sign) was smaller than 1, the exponent is negative. If it was bigger than 1, the exponent is positive

9 4.3 An Application of Exponents: Scientific Notation
Converting to scientific notation (examples): Converting back – just undo the process:

10 4.3 An Application of Exponents: Scientific Notation
Multiplication with scientific notation: Division with scientific notation:

11 4.4 Adding and Subtracting Polynomials; Graphing Simple Polynomials
When you read a sentence, it split up into words. There is a space between each word. Likewise, a mathematical expression is split up into terms by the +/- sign: A term is a number, a variable, or a product or quotient of numbers and variables raised to powers.

12 4.4 Adding and Subtracting Polynomials; Graphing Simple Polynomials
Like terms – terms that have exactly the same variables with exactly the same exponents are like terms: To add or subtract polynomials, add or subtract the like terms.

13 4.4 Adding and Subtracting Polynomials; Graphing Simple Polynomials
Degree of a term – sum of the exponents on the variables Degree of a polynomial – highest degree of any non-zero term

14 4.4 Adding and Subtracting Polynomials; Graphing Simple Polynomials
Monomial – polynomial with one term Binomial - polynomial with two terms Trinomial – polynomial with three terms Polynomial in x – a term or sum of terms of the form

15 4.5 Multiplication of Polynomials
Multiplying a monomial and a polynomial: use the distributive property to find each product. Example:

16 4.5 Multiplication of Polynomials
Multiplying two polynomials:

17 4.5 Multiplication of Polynomials
Multiplying binomials using FOIL (First – Inner – Outer - Last): F – multiply the first 2 terms O – multiply the outer 2 terms I – multiply the inner 2 terms L – multiply the last 2 terms Combine like terms

18 4.6 Special Products Squaring binomials: Examples:

19 4.6 Special Products Product of the sum and difference of 2 terms:
Example:

20 4.7 Division of Polynomials
Dividing a polynomial by a monomial: divide each term by the monomial

21 4.7 Division of Polynomials
Dividing a polynomial by a polynomial:


Download ppt "4.1 The Product Rule and Power Rules for Exponents"

Similar presentations


Ads by Google