College Algebra
posted by Krissy on .
Last one for today! Again would appreciate a breakdown on how to get to a resolution. It is multiple choice.
1. Simplify the expression using the quotient to a power property. (3y^6/z^7)^3
a. 27y^9/z^7
b. 3y^9/z^10
c. 27y^18/z^7
d. 27y^18/z^21
2. Use a descriptive variable and an inequality symbol to write a model for the statement. The Thompson family will spend more than 14,000 on home improvement.
a. Let a represent the amount. a < $14,000
b. Let a represent the amount. a < $14,000
c. Let a represent the amount. a > $14,000
d. Let a represent the amount. a > $14,000
3. Simplify and subtract (if possible). 10ã27xã75x
a. 25ã3x
b. 10ã48x
c. 25xã3
d. Cannot be subtracted
4. Rewrite the expression as a single term. 1/r1/s+1/t
a. St+rtrs/rs+t
b. 1/rs+t
c. St+rtrs/rst
d. Strt+rs/rst
5. Factor the difference of perfect cubes completely. 27a^31000
a. (3a+10)(9a^2100)
b. (3a10)(9a^2+100)
c. (3a+10)(9a^230a+100)
d. (3a10)(9a^2+30a+100)

(3y^6/z^7)^3
3^3 (y^6)^3 / (z^7)^3
27 y^18/z^21
(D)
"more than" means greater
don't know why a&b and c&d are the same, but (C) or (D) works for me. I assume there should have been <= or >= in there. You want just ">" since we want "more," not just "at least".
10√27x√75x
10√9√3x  √25√3x
10*3√3x  5√3x
25√3x
(A)
1/r1/s+1/t
put over a common denominator: rst
st/rst  rt/rst + rs/rst
(strt+rs)/(rst)
(D) assuming the usual sloppiness with parentheses
27a^31000
(3a)^3  10^3
(3a10)(9a^2+30a+100)
(D)