Easy Algebra Step-by-Step

220 Answer Key

Chapter 7 Rules for Exponents

Exercise 7

1. 
   

   x^4 x^9 = x^13

   
   


2. 
   

   x^3 x^4 y^6 y^5 = x^7 y^11

   
   


3. 
   

x

x

x

6

3

=^3

4. 
   

xy

xy

xy

(^55) y
(^24) y
=^3
5.
x
x
x
x
4
6
2
2
1
==x−

6. (x^2 )^5 = x^10


7. (xy)^5 = x^5 y^5


8. (−5x)^3 = −125x^3


9. (2x^5 yz^3 )^4 = 16x^20 y^4 z^12
   10.^5
   3

625

81

4

x x^4

⎛

⎝⎜

⎛⎛

⎝⎝

⎞

⎠⎟

⎞⎞

⎠⎠

=

11.

⎛−

⎝⎜

⎛⎛

⎝⎝

⎞

⎠⎟

⎞⎞

⎠⎠

=

3

5

81

625

(^44)
4
x
y
x
y

12. (2x + 1)^2 is a power of a sum. It
    cannot be simplifi ed using only rules
    for exponents.


13. (3x – 5)^3 is a power of a difference. It
    cannot be simplifi ed using only rules
    for exponents.


14. (x + 3)(x + 3)^2 = (x + 3)^3

15.

5

5

()^2 xy 10

() 2 xy

=() 22 xyx

1

Chapter 8 Adding and Subtracting Polynomials

Exercise 8

1. x^2 − x + 1 is a trinomial.


2. 125x^3 – 64y^3 is a binomial.


3. 2x^2 + 7 x − 4 is a trinomial.


4. −

1

3

xy^525 is a monomial.

5. 2x^4 + 3 x^3 −7x^2 – x + 8 is a polynomial.


6. −15x + 17 x = 2 x


7. 14xy^3 – 7x^3 y^2 is simplifi ed.


8. 10x^2 – 2x^2 – 20x^2 = −12x^2


9. 10 + 10 x is simplifi ed.


10. 12x^3 − 5x^2 + 10 x − 60 + 3 x^3 −
    7 x^2 − 1
    = 15 x^3 − 12x^2 + 10 x − 61
    11. (10x^2 – 5x + 3) + (6x^2 + 5 x − 13)
    = 10 x^2 – 5x + 3 + 6 x^2 + 5 x − 13
    = 16 x^2 − 10
    12. (20x^3 − 3x^2 − 2x + 5) +
    (9x^3 + x^2 + 2 x − 15)
    = 20 x^3 − 3x^2 − 2x + 5 + 9 x^3 + x^2 +
    2 x − 15
    = 29 x^3 – 2x^2 − 10
    13. (10x^2 − 5x + 3) − (6x^2 + 5 x − 13)
    = 10 x^2 − 5x + 3 − 6x^2 − 5x + 13
    = 4 x^2 − 10x + 16
    14. (20x^3 − 3x^2 − 2x + 5) −
    (9x^3 + x^2 + 2 x − 15)
    = 20 x^3 − 3x^2 − 2x + 5 − 9x^3 − x^2 −
    2 x + 15
    = 11 x^3 − 4x^2 − 4x + 20