Integral and Rational Exponents PDF

GOOD MORNING!! laws for integral and rational exponents! WARM UP ACTIVITY You have one minute to simplify each expression show your work or be ready to explain how you found your answer 2 2 1 3 1. 4 2. 3...

GOOD MORNING!! laws for integral and rational exponents! WARM UP ACTIVITY You have one minute to simplify each expression show your work or be ready to explain how you found your answer 2 2 1 3 1. 4 2. 3 3 3. 1 5 5 ANSWERS! Check your answer share with your group your work or explanation 1. 16 2. 27 3. 5  VOCABUL ARY Base 2 Exponen Expression x t or power  INTEGRAL EXPONENTS exponents which are whole numbers that can be either negative, positive or a zero  INTEGRAL EXPONENTS Positive negative zero 2 -2 0 x x x  RATIONAL EXPONENTS exponents which are expressed in ratio or fraction (a/b).  RATIONAL EXPONENTS 1/ 5/7 6/1 3/8 x2 x x1 x  RULES OR L AWS integral exponents NOte: ! The following rules only apply when you have the same base PRODUCT RULE: What do? do i Why does it work? when multiplying with the same base, add the exponents 2 3 x x xx xxx Example: 5 x QUOTIENT RULE: What do? do i When dividing with the same Why does it work? base, subtract exponents. 5 x x x x x 2 Example: 3 = = x x x x x POWER OF A POWER: What do? do i Why does it work? when applying an exponent inside parenthesis, multiply 2 3 exponents (x 2 2 2 x )x x Example: 6 x POWER OF A PRODUCT: What do? do i Why does it work? when applying an exponent to a product, apply to each base 3 (2x) 2x 2x 2x Example: 3 8 x  c ac x ac - bc POWER OF A ( ) x bc =x QUOTIENT: What do i do? when applying an exponent to a How does it work? Quotient, apply to each base then proceed to quotient rule if applicable. 3 15 ( 5 x x 6 Example: 3 3 = 9 =x x ( )x 6 x ) ZERO EXPONENT: What do? do i Why does it work? Anything to the zero equals one 3 x 0 Example 3 = x = 1 x NEGATIVE EXPONENT: What do i do? Flip the base in a fraction and examples: change the sign of the exponent Pro tip: in simplest form, exponents are positive  RULES OR L AWS rational exponents NOte: ! The following rules only apply when you have the same base RATIONAL FRACTIONAL EXPONENT OR What do i EXPONENT: do? Inside exponent goes on top, outside examples: exponent goes on bottom Pro tip: fractional exponents make it easier to use other exponent rules PRACTIC E: be ready to show your work or explain how you found your answer 6 2 x 2 x 1. 2 2. ( x) 3. 5 x x 6 5 3 4. x x 5. (x 6 0 6. (4x) ) ANSWER KEY: Check your answer & share with your group your work or explanation 4 1 1. x 2. x 3. 3 x 11 3 4. x 5.1 6. 64x QUIZ: be ready to show your work or explain how you found your answer 10 5 x 3 3 x 1. 12 2. ( x) 3. 2 x x 3 6 3 4. x x 5. (x 3 -2 6. (3/5 ) ) QUIZ: be ready to show your work or explain how you found your answer 6 1 2 4 x 7. -5 8. ( x) 9. 8 x x 10 7 2 -9 1 x x 1 (x 4 1/ 4 1 (x/y) 0. 1. ) 2.