Chapter 5 Study Guide 5-1 Study Guide - Operations with Polynomials Multiply and Divide Monomials Negative exponents are a way of expressing the multiplicative inverse of a number. Negative Exponents = and = for any real number a 0 and any integer n. ≠ When you simplify an expression, you rewrite it without powers of powers, parentheses, or negative exponents. Each base appears only once, and all fractions are in simplest form. The following properties are useful when simplifying expressions. = for any real number and integers and Product of Powers a m n. Quotient of Powers = for any real number a 0 and integers m and n. ≠ For a, b real numbers and m, n integers: = Properties of Powers = = b 0 ≠ = or a 0,b 0 ≠ ≠ Example: Simplify. Assume that no variable equals 0. a. ( ( = 25 b. = 75 = = = = 75 = – Exercises: Simplify. Assume that no variable equals 0. 1. 2. 3. 4. 5. 6. 7. 8. 9. 4j(–)(3) 10. 11. 12. 5-1 Study Guide (continued) Operations with Polynomials Polynomial a monomial or a sum of monomials
Chapter 5 Study Guide 5-1 Study Guide - Operations with Polynomials Multiply and Divide Monomials Negative exponents are a way of expressing the multiplicative inverse of a number. Negative Exponents = and = for any real number a ≠ 0 and any integer n. When you simplify an expression, you rewrite it without powers of powers, parentheses, or negative exponents. Each base appears only once, and all fractions are in simplest form. The following properties are useful when simplifying expressions. Product of Powers = for any real number a and integers m and n. Quotient of Powers = for any real number a ≠ 0 and integers m and n. Properties of Powers For a, b real numbers and m, n integers: = = = b ≠ 0 = or a ≠ 0,b ≠ 0 Example: Simplify. Assume that no variable equals 0. a. ( ( = 25 = 75 = = 75 b. = = = – Exercises: Simplify. Assume that no variable equals 0. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 4j(–)(3) 12. 5-1 Study Guide (continued) Operations with Polynomials Polynomial a monomial or a sum of monomials
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