advertisement

HW 5.1/5.3 - Algebra 2 Name: ___________ Properties of Exponents: Keep the ______________. __________________ the exponents. Use when the expression has only multiplication or division. Give any bases without any exponent, an exponent of 1. Repeated bases: Keep the bases and add or subtract the exponents. Ex: (x4)(x3) = x12 Outside powers: Multiply the exponent of each base inside the parentheses by the outside exponent. Ex: (2a5b2)3 = 21·3a5·3b2·3 = 23a15b6 = 8a15b6 Negative Exponents: Change the position, numerator/denominator, of the base and make the 3 p 5 31 p 5 31 q 4 3q 4 exponent positive. Positive exponents stay in their positions. Ex: 7q 4 71 q 4 71 p 5 7 p 5 Zero Exponents: Any bases with an exponent of zero are equal to 1. Ex: 5x0y3 = 51(1)y3 = 5y3 Operations with Polynomials: Use when there are addition or subtraction signs in the expression. Add or subtract like terms. Ex: (5x2 – 3x + 6) – (x2 – 2x + 8) = 4x2 + x – 2 Multiply by distributing. Ex: (3x – 8)(x + 7) = 3x2 + 21x – 8x – 56 = 3x2 + 13x – 56 Write out polynomials the same number of times if there is an exponent outside parentheses. Ex: (x + 3)4 = (x + 3) (x + 3) (x + 3) (x + 3) Simplify. 1. (7gh5)3 2. (3c6d2)(8c5d) (5m) 2 3. 7 p 8 4. (4x – 9) – (3x – 2) 5. (4x – 9) + (3x – 2) 6. (4x – 9)(3x – 2) 8. (x – 8)2 9. (-8x)2 x2 y 7. 3 4 x y 1 10. 3x-4y 11. (3xy)-4 12. 3(xy)-4 7( j 5 k 2 ) 0 13. 21 jk 7 14. –(y + 7)2 16. 3b(b + 1)2 17. (x – 9)(7x2 – x + 3) 19. (2x – 5)3 20. (8x3y2 + 5x2y + 3xy) + (-7x2y – xy) – (9x3y2 – 11xy + 4) 15. (4v 2 w 3 ) 3 3(v 5 w 2 ) 2 18. (x – 9) – (7x2 – x + 3)