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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:

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

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

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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

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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

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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

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Quotient Rule for Exponents Examples: 10.1 – Exponents

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What is the Rule? 10.1 – Exponents Zero Exponent

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

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Examples: 10.2 – Negative Exponents

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

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Examples: 10.2 – Negative Exponents

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Practice Problems 10.2 – Negative Exponents

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Practice Problems 10.2 – Negative Exponents

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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

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Scientific Notation Examples: 10.2 – Negative Exponents

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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. 10.3 – Polynomials

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Definitions Monomial: a polynomial with exactly one term. Binomial: a polynomial with exactly two terms. Trinomial: a polynomial with exactly three terms. 10.3 – Polynomials

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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. 10.3 – Polynomials

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Practice Problems Identify the degrees of each term and the degree of the polynomial. 10.3 – Polynomials

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Combining Like Terms - Practice Problems Simplify each polynomial. 10.3 – Polynomials

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Practice Problems Simplify each polynomial. 10.3 – Polynomials

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Practice Problems Evaluate each polynomial for the given value. 10.3 – Polynomials

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