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College Algebra

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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). 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)

  • College Algebra - ,

    3^3 (y^6)^3 / (z^7)^3
    27 y^18/z^21

    "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√9√3x - √25√3x
    10*3√3x - 5√3x

    put over a common denominator: rst

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

    (3a)^3 - 10^3

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