4.1 The Product Rule and Power Rules for Exponents

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:

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:

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

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

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

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

4.2 Integer Exponents and the Quotient Rule • Examples:

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

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

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

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.

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.

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

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

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

4.5 Multiplication of Polynomials • Multiplying two polynomials:

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

4.6 Special Products • Squaring binomials: • Examples:

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

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

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

4.1 The Product Rule and Power Rules for Exponents