220 Answer Key
Chapter 7 Rules for Exponents
Exercise 7
x^4 x^9 = x^13
x^3 x^4 y^6 y^5 = x^7 y^11
x
x
x
6
3
=^3
xy
xy
xy
(^55) y
(^24) y
=^3
5.
x
x
x
x
4
6
2
2
1
==x−
- (x^2 )^5 = x^10
- (xy)^5 = x^5 y^5
- (−5x)^3 = −125x^3
- (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
- (2x + 1)^2 is a power of a sum. It
cannot be simplifi ed using only rules
for exponents. - (3x – 5)^3 is a power of a difference. It
cannot be simplifi ed using only rules
for exponents. - (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
- x^2 − x + 1 is a trinomial.
- 125x^3 – 64y^3 is a binomial.
- 2x^2 + 7 x − 4 is a trinomial.
- −
1
3
xy^525 is a monomial.
- 2x^4 + 3 x^3 −7x^2 – x + 8 is a polynomial.
- −15x + 17 x = 2 x
- 14xy^3 – 7x^3 y^2 is simplifi ed.
- 10x^2 – 2x^2 – 20x^2 = −12x^2
- 10 + 10 x is simplifi ed.
- 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