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Chapter 5, Section 1 Exponents We will use mainly rational numbers for bases and integers for exponents in this class – in College Algebra and higher level courses you will begin using fractions as exponents. Please note that fractional exponents follow the same rules as integer exponents. Conventionally, exponents are reported as whole number whenever possible. Rule one The Product Rule If factors have the same base, you may simplify by adding the exponents. x s x t x st example: 2 2 23 4(8) 32 25 Practice Problems: x 5 (x 3 ) 2x 5 (3x 2 ) Rule Two The Quotient Rule If a factor in the numerator and a factor in the denominator have the same base, you may subtract the exponents – you must subtract the exponent in the denominator from the exponent in the numberator. xs x st t x Some facts that come about through the quotient rule: x0 1 x 1 1 x Examples 57 53 x 11 x7 75 75 x3 x4 x 3 (x 7 ) x 2 32 x 5 31 x 2 Rule 3 The Power Rules 3A ( xy ) p x p y p (3x) 3 33 x 3 27x 3 example 3B ( x s ) t x st ( x 2 ) 5 x 10 example p 3C x xp p y y 3 example Problems 3 1 5 2 2x 1 (2x ) 1 ab 2 (ab) 3 abc 2 2 ab1 x (2x ) 2 y 3 6x 1 y 5 x y 1 8 2 27 3 report your answers with whole number exponents 2 1 (2) 0 20 22 3 1 2 2 ( xy ) 5 4x 3 5x 3 y 2 (5xy ) 2 x 2 (2xy 2 ) 3 2 1 x 2 y 1 x 2 3 y 2 (2x 1 ) 2 (2x ) 2 (2x ) 2 (3y) 1 (3x 2 y 1 ) 2 (32 y) 1