Assignment 2.1. Exponent Properties: The Product Rule
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1 Assignment.1 NAME: Exponent Properties: The Product Rule What is the difference between x and x? Explain in complete sentences and with examples. Product Repeated Multiplication Power of the form a b x 9 x 6 Determine the general rule for what happens when we have two exponential expression multiplying each other with the same base. Write the rule in words. Why do you think this rule is called the product rule? Write the algebraic rule. Exponent Properties: The Distributive Rule for Products Product Repeated multiplication Commutative Property to align like bases ( ) ( )( )( ) ( 6) (x y) 5 ( 5) (x) 6 Determine a general rule for two monomials raised to a power. Write the rule in words. Power of the form a c b d Why is this rule called the Distributive Rule? How is this rule different from the product rule? Write the algebraic rule: Secondary Math II
2 Exponent Properties: The Quotient Rule Quotient Repeat Multiplication Cancel Power in form a b x 10 x 5 1 y 0 Too big to write out! Find another way. 5 7 y 8 Determine a general rule for two exponential expressions dividing each other with the same base. Write the rule in words. Write the algebraic rule. Exponent Properties: The Zero Exponent Rule Quotient Repeated Multiplication Power in form of a b Solved x 7 x 7 y 0 y 0 Too big to write. Find a new way. What is the rule for anything raised to the zero power? Exponent Properties: The Power Rule Problem 1 st Repeated Multiply nd Repeated Multiply Power in the form a c ( ) (5 ) x 6 x 6 x 6 x 6 ( 5 y ) (a 0 ) To big. Find a new way Determine the general rule for a power raised to a Power. Write the rule in words. 7 1 How is this rule different from the product rule? Write the algebraic rule Secondary Math II
3 Exponent Properties: Negative Exponents Quotient Repeated Multiplication Answer as a fraction Power in the form a b 5 a a 9 1 a b 5 a 9 b c 1 f 5 c 1 f x x x y x x x x x x x What does a negative exponent mean? 8 Are positive expressions with negative exponents negative? Explain. What do you think this simplifies to be: 1? Make a guess or try to work it out mathematically. Write the algebraic rule. Review 1) (y + y) + (y 5y + ) ) (5c + 7c + 1) + (c 6c + 8) ) ( x + x + 1)(x 8x + ) ) (y + 6y 1)(y 11y + ) 5) (t ) 6) (y + ) Secondary Math II
4 Assignment. Simplify each expression t t. 5 9 x x 5. 5 x 6. ( 6x )( x ) x 7. ( x y )(-6 y ) 8. (5p )( m p ) 9. (10g h v )(11gh ) 9. (x ) 10. ( p ) ( x m ) 1. ( x ) 1. ( a ) 1. ( x ) 15. ( 10 ) 16. ( x 6 5 ) 17. ( 7 j ) 8 a 18. a b 0. b 5 10 x 1. x 9 c. 6c x y. y 8. 6 c d x x 6. x Secondary Math II
5 Assignment. Simplify the expression 1. x x. x x 6 y 0. (x 8 ). n n 5 5. ( a b ) 6. m m 7. m m 8. ( x y ) 5 ( x y ) 9. n n 10. v vx 11. ( y ) 5 1. (a b 5 ) 1. (w x )(w 6 x 1 ) 1. (5s t ) 15. (x )(x ) 16. w w c d 9cd (rs 0 ) ( f h )( 5 f )( h ) 0. x y ( ) x y 1. 8x x. x y 5 1 a b.) 5 5 a b.) 1 5 5x y z ) ( g g ) 6.) c 8d ) x y 8 11 (x ) ( x ) 8.) 11 8x 9.) (x-5) Secondary Math II
6 Assignment. Simplify each radical expression x y x y 8. 7x 5 y x y x mn 1. 56b c 7 Find each sum or difference x y x Secondary Math II
7 Assignment.5 Find each product. Simplify each expression fully ( ) 6. ( 6 + 5) 7. 5( 10 + ) 8. 6( + ) 9. ( )( + ) 10. ( )( + 5) (1 + )( 15. ( 6 + 5) 16. ( + ) 17. ( + ) x 0. ( + 5) -7- Secondary Math II
8 Assignment.6 Write each expression in radical form x 1. 6 / 5. (x) /5 6. (9x y) 8/7 7. (a 7 n ) / 8. (xyz 9 ) 11/ 9. (5c d f 7 ) 6/5 Write each expression in exponential form. 10. ( ) ( w 7 ) x 7 1. ( x ) 15. 9n ( a ) v n 19. Radical Form Exponent Form Simplified Form 8 7x 6 (5x ) 1x (16x ) (18x ) 1 0. (9 ) 1 1. (789 9 ) 1 9. (9 7 ) 7. x x 6 y 5. x 5 y 8 z 1-8- Secondary Math II
9 Assignment.7 Simplify Write the expression as a complex number in standard form Write the expression as a complex number in standard form. 9. (6 i) + (5 + i) 10. ( 1 + i) + ( 9 i) 11. ( 1i ) + ( 7i + 6) 1. (i 10) + (7 8i) 1. ( 6i) ( 6i) 1. ( 1 + i) (7 5i) -9- Secondary Math II
10 Assignment.7 (Continued) 15. (6i + ) (10i + 8) 0. (8 i)( + i) 16. (i 8) (11 + 7i) 1. ( + i)( i) 17. 6i( + i). ( i)(11 + 6i) 18. i( 7i + 1). ( + i)( i) 19. i( 10i). ( 5 i)( 5 + i) -10- Secondary Math II
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Skills Practice Skills Practice for Lesson 4.1
Skills Practice Skills Practice for Lesson.1 Name Date Thinking About Numbers Counting Numbers, Whole Numbers, Integers, Rational and Irrational Numbers Vocabulary Define each term in your own words. 1.
Equations. Rational Equations. Example. 2 x. a b c 2a. Examine each denominator to find values that would cause the denominator to equal zero
Solving Other Types of Equations Rational Equations Examine each denominator to find values that would cause the denominator to equal zero Multiply each term by the LCD or If two terms cross-multiply Solve,