Quotients of Monomials/Zero and Negative Exponents
5.1 p. 214 #25
Simplify.
(a^(2m)b^(2m+1))/((a^2b^2)^m
b
5.3 pg 223 #12
Write the following in scientific notation
4775 times 10^(-2)
4.755times10^(-5)
5.5 pg. 234 #11
Simplify without negative or zero exponents
(x(x-1))/(x-2)^2divide(x-1)^2/(x-2)
x/((x-2)(x-1))
5.7 pg 239 #1
Simplify
(1-1/3)/(1/2-1/6)
2
5.8 pg 245 #9
Solve
y^2/4-(3y)/2+2=0
{2,4}
5.1 p. 214 #30
Simplify
(a^(n-1)b^(2n))/(a^(n+1)(b^2)^(n-1)
(b^2)/a^2
5.4 pg 228 #3
Simplify
((u^2-u-2))/(u^2+u)
(u-2)/u
5.6 pg 237 #17
Simplify
a/(bc)+b/(ac)+c/(ab)
(a^2+b^2+c^2)/(abc)
5.7 pg 239 #11
(1/x^2-1/y^2)/(1/x^2+2/(xy)+1/y^2)
(y-x)/(y+x)
5.9 pg 249 #9
Solve and check. If there is no solution say so
(6t^2-t-1)/(3(t^2+1))=2
{-7}
5.2 p. 219 #40
Simplify without negative or zero exponents
((a^0)/b)^(-2)((a)/b^(-2))^(-2)
1/(a^2)
5.3 pg. 223 #29
Simplify, assuming that the factors are approximations. Give answers in scientific notation with the same number of significant digits as the least accurate factor.
((8times10^(6))(2times10^(-2)))/(4times10^2)
4times10^2
5.5 pg 234 #23
Simplify without negative or zero exponents
(a^4+2a^2b^2+b^4)divide(a^4-b^4)*(a-b)
(a^2+b^2)/(a+b)
5.7 pg 239 #15
Simplify
(s^2-t^(-2))/(s-t^(-1))
(st+1)/t
5.9 pg 250 #29
Solve and check. If there is no solution say so
(1/x^2-x^2)/(1/x+x)=3/2
{-2,1/2}
5.2 p. 219 #42
Simplify with no negative or zero exponents
((u^2)/v)^2+(-u^(-2)v)^(-2)
(2u^4)/v^2
5.4 pg. 229 #43
Simplify
(x^(2n)-2x^ny^n+y^(2n))/(x^(2n)+3x^ny^n-4y^(2n))
(x^n-y^n)/(x^n+4y^n)
5.6 pg 237 #35
Simplify
1/(2u^2-3uv+v^2)+1/(4u^2-v^2)
(3u)/((2u-v)(2u+v)(u-v)
5.7 pg 240 #25
Simplify
(1-(2-1/x)/x)/(1-1/x)
(x-1)/x
5.8 pg 246 #21
The rail line between two cities consists of two segments, one 96 km longer than the other. A passenger train averages 60km/h over the shorter segment, 120 km/h over the longer, and 100 km/h for the entire trip. How far apart are the cities?
d1 = x
d2 = x+96
dt = 2x+96
x/60+(x+96)/120 = (2x+96)/100
x=32
160km apart
5.2 p. 220 #49
Replace the (?) by a polynomial to make the statement true
4-5x^(-1)+x^(-2)=x^(-2)(?)
4x^2-5x+1
5.4 pg 229 #27
Find the (a) domain of each function and (b)its zeros if any
(x^3-2x^2+x-2)/(x^4+x^2-2)
(a)Reals except -1
(b) zeros x= 1,2
5.6 pg 237 #41
Find constants A and B that make the Equation true
(x-7)/(x^2+x-6)=A/(x+3)+B/(x-2)
A=2
B=-1
5.7 pg. 241 #33
Simplify
(x/(x+1))/((x/(x+1))+1
x/(2x+1)
5.9 pg 251 #17
A train averaged 120km/h for the first two thirds of a trip and 100km/h for the whole trip. Find its average speed for the last third of the trip.
1/180+1/(3x)=1/100
75km/h