10.1 – Exponents Notation that represents repeated multiplication of the same factor. where a is the base (or factor) and n is the exponent. Examples:

Product Rule for Exponents If m and n are positive integers and a is a real number, then Examples: 10.1 – Exponents

Power Rule for Exponents If m and n are positive integers and a is a real number, then Examples: 10.1 – Exponents

Power of a Product Rule If m, n, and r are positive integers and a and b are real numbers, then Examples: 10.1 – Exponents

Power of a Quotient Rule If m, n, and r are positive integers and a and c are real numbers (c does not equal zero), then Examples: 10.1 – Exponents

Quotient Rule for Exponents If m and n are positive integers and a is a real number and a cannot equal 0, then Examples: 10.1 – Exponents

Quotient Rule for Exponents Examples: 10.1 – Exponents

What is the Rule? 10.1 – Exponents Zero Exponent

If a is a real number other than 0 and n is an integer, then Problem: 10.2 – Negative Exponents

Examples: 10.2 – Negative Exponents

If a is a real number other than 0 and n is an integer, then Examples: 10.2 – Negative Exponents

Examples: 10.2 – Negative Exponents

Practice Problems 10.2 – Negative Exponents

Practice Problems 10.2 – Negative Exponents

Scientific Notation A number is written in scientific notation if it is a product of a number a, where and an integer power r of 10. Examples: 10.2 – Negative Exponents

Scientific Notation Examples: 10.2 – Negative Exponents

Definitions Coefficient: the numerical factor of each term. Constant: the term without a variable. Term: a number or a product of a number and variables raised to a power. Polynomial: a finite sum of terms of the form ax n, where a is a real number and n is a whole number – Polynomials

Definitions Monomial: a polynomial with exactly one term. Binomial: a polynomial with exactly two terms. Trinomial: a polynomial with exactly three terms – Polynomials

Definitions The Degree of a Term with one variable is the exponent on the variable. The Degree of a Term with more than one variable is the sum of the exponents on the variables. The Degree of a Polynomial is the greatest degree of the terms of the polynomial variables – Polynomials

Practice Problems Identify the degrees of each term and the degree of the polynomial – Polynomials

Combining Like Terms - Practice Problems Simplify each polynomial – Polynomials

Practice Problems Simplify each polynomial – Polynomials

Practice Problems Evaluate each polynomial for the given value – Polynomials