simplifying expressions, square roots; factoring

[yohanson77]

Hello,

It's been a while since I was on here as I've been going through my maths book for the past month. Now I'm hitting some problems and hope somebody can help. I've got seven questions I'm stuck on and I'll post them as one topic to save flooding the forum. Sorry if they are hard to understand, I tried to paste from word but it went all wrong.

Q1. Simplify x^4 * x^3 / x^-3 * x^-2 / x^5

Q2. Simpify a^4 * (a^3)^3 / (a^5)^-2

Q3. Simplify sqrt 6300

Options: A. 10 sqrt 63 B. 30 sqrt 7 C. 100 sqrt 63 D. 3 sqrt 700

Q4. Simplify (3 sqrt 2 - 2 sqrt 3) (2 - sqrt 6)

Q5. Rationalize the expression (3 sqrt 7 - sqrt 5) / (2 sqrt 5 - sqrt 7)

Q6. Simplify {(27x^2y)^1/3 (xy^2)^1/2} / {(4x^-2y^2)^1/2 x ^3/2}

Options: A. 3/2 x^2/3 y^1/3
B. 3/2 x^11/3 y^1/3
C. 3x^2/3 y^1/3
D. 9/2 x^2/3 y^1/3

Q7. Factorise 9pr^2 t^2 - 12prst^2 + 4ps^2 t^2 - pq^2 t^2

This is the last topic in the book and these are the warmer questions, help would be appreciated to get me started. Everyone who helped me last month thanks again, didn't hit many hurdles.

Yours

Yohanson

 

[Gene]

x^4 * x^3 / x^-3 * x^-2 / x^5
Start by putting everything in the numerator by changing the signs of the denominator exponents.
x^4 * x^3 * x^3 * x^2 * x^-5
That should get you started on most of the rest.

 

[yohanson77]

x^4 * x^3 / x^-3 * x^-2 / x^5
Start by putting everything in the numerator by changing the signs of the denominator exponents.
x^4 * x^3 * x^3 * x^2 * x^-5
That should get you started on most of the rest.

Thanks gene, will have a go at them. I just hope I pick this up, they look really hard:-(

 

[yohanson77]

O.k, now I'm stuck on Q4 to Q7. Have slowly worked out Q1 to Q3 and It's quite easy when shown. Thanks again Gene

 

[Gene]

Q4: Best I see is to multiply it out. You get two sqrts (12 & 18) that you can factor out squares (4 & 9) then gather terms.

Q5: Multiply top and bottom by
2sqrt(5)+sqrt(7)
That gets rid of sqrts in the denominator.

Q6: pretty much like Q1. bring the outer exponents into the ()s first. Forinstance
(27x^(2)y)^(1/3) =
3x^(2/3)y^(1/3)
Do the same to the rest then put them on top and gather terms.

Q7: The only thing common is pt^2. Pull that out in front of ()s around the rest.