Last one for today! Again would appreciate a breakdown on how to get to a resolution. It is multiple choice.

Question

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). 10�ã27x-�ã75x
a. 25�ã3x
b. 10�ã48x
c. 25x�ã3
d. Cannot be subtracted

4. Rewrite the expression as a single term. 1/r-1/s+1/t
a. St+rt-rs/r-s+t
b. 1/r-s+t
c. St+rt-rs/rst
d. St-rt+rs/rst

5. Factor the difference of perfect cubes completely. 27a^3-1000
a. (3a+10)(9a^2-100)
b. (3a-10)(9a^2+100)
c. (3a+10)(9a^2-30a+100)
d. (3a-10)(9a^2+30a+100)

Answer 1

(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/r-1/s+1/t
put over a common denominator: rst

st/rst - rt/rst + rs/rst
(st-rt+rs)/(rst)
(D) assuming the usual sloppiness with parentheses

27a^3-1000
(3a)^3 - 10^3
(3a-10)(9a^2+30a+100)
(D)