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2.2 Properties of Exponents • Objectives: – Evaluate expressions involving exponents. – Simplify expressions involving exponents. • Standard: – 2.1.11.A. Use operations (e.g. raising to a power). The expression an is called a power of a. In the expression, a is called the base and n the exponent. • I. Definition of Integer Exponents • Let a be a real #. • If n is a natural #, then an = a * a * a . . * a, n times. • If a is nonzero, then a0 = 1. • If n is a natural #, then a n 1 n a Properties of Exponents Let a and b be nonzero real numbers. Let m and n be integers Product of Powers a a Quotient of Powers am mn a n a m n a Power of a Power a a Power of a Product ab a nb n m n n n Power of a Quotient mn a a n b b n m n Examples: 1. Simplify 3x 2 y 2 2 x 3 y 4 . Write your answer wit h positive exponents only. * 2. Simplify 2 z 3x 2 5 z 3 . Write your answers with positive exponents only. * 4 y 3. Simplify 12 3 . Write your answer wit h positive exponents only. 2z y 7 . Write your answer wit h positive 5 3 2 4. Simplify - 2a b -3b c 5. Simplify 2 7 cb 2 5 3 exponents only. . Write your answer wit h positive exponents only. 6. Simplify x -3 y -1 x 1 3 2 y 0 . Write your answer wit h positive exponents only. 3 12 3 3z 3x yz . Write your answer wit h positive exponents only. 7. Simplify 4 7 x 2 xy 2 Rational Exponents An expression with rational exponents can be represente d in an equivalent form that involves the radical symbol, For example, a 1 3 3 . 1 equals a because when a 3 is cubed, the result is a, as as shown in your notes. This is the definition of 3 a . Definition of Rational Exponents For all positive real numbers a : 1 If n is a nonzero integer, a n n a . If m and n are integers and n 0, m 1 a n (a n )m (n a )m Example 1 a. 16 b. 27 4 c. 125 d. 8 2 f. 36 3 1 3 e. 64 3 81 5 4 1 3 2 4 3 2 4 216 Writing Activities: 1). Describe how to use Properties of Exponents to simplify 307 36. 1/ 2 2). Explain why 25 and -5 are not equivalent. Homework Integrated Algebra II: Section 2.2 Level A Honors Algebra II: Section 2.2 Level B PSSA WARM-UP QUESTION Algebra II - Chp. 2 Standard 2.1.11 A Find Powers. • What are some of the properties of exponents? Properties of Exponents Multiplication of Exponents Power to a Power Division of Exponents Raised to Zero Negative Exponent Rule Example Example 1 • The equation for centripetal acceleration is given as: Ac 4 2 RT 2 1b. Find the centripetal acceleration in ft. per second squared of a rider who makes one rotation in 5 seconds and whose radius is 6 feet. r = 6, T = 5 Ac = 9.47 feet per second squared