Download Solutions

Solutions
Algebra Set #1
Solutions and comments in blue font
Problems to Do:
1. Simplify each to a single fraction or number:
a)
7
3
4
9
1


5 2 / 3 15
70/431
b) (2/3)3 ÷( (1 – 7/8)2 + ½ )
8x10
c) (2*108)3
d)
(2*104)4
÷ (4*102)2
4096/6939
24
1012
2. Simplify each expression below as much as possible; your answer should have
positive exponents only.
a. (a3b-2)-3(a2b-2)(a-2b-1)-1
b5/a5
b) (x-1 – y-1)-1(x-1y-1)-1 xy/(1/x –
1/y) or also x2y2/(y-x)
c) (x +y)-2(x +y)3(x2y3)-2 (x+y)/(x4y6)
2
3
 a 2   a 2 

 

 4   b 1c 2 
 

d)  bc
1/ (a2bc14)
3
Please simplify each of the following expressions as much as possible
a) 1252/3 25 b) 3-2 1/9
31252/5 25 (3125 = 55)
c) 45/2 32 d) 27-4/3 1/81
e) (-1)5331 -1 f)
4.Given that 1 meter = 39 inches, what is the distance to the Sun in kilometers if the
distance in miles is assumed to be 93 million?
Please show all steps leading to your answer and pay close attention to units.
1 mile = 5280 feet =5280 x12 inches
=5280 x12/39 meters
so 93 million miles = 93 x106 x 5280 x12/39 meter
= (93 x 528 x 12 /39) x 107 meters
= (15108.9231) x 107 m
= 1.511 x 1011 meters (rounded)
but 1000 meters = 1 kilometer = 1 km so this is equal to
1.511 x 108 km
5. Is it true in general that
a) (x y)n = xnyn ? (n a positive integer) YES
b) (x + y )n = xn + yn ? NO unless n =1
counterexample: (x +y)2 =
(x+y)(x+y) = x2 + 2xy + y2 not x2 + y2
c) 1/x + 1/y = 1/(x+ y) NO counterexample: 1/2 + 1/5 = 7/10 not 1/7
if your answer to any of them is no, provide a counterexample.