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)