Math help easy ten points?

Question

i have a few questions for math please help me....

1) (x^2 y^-3 z^-1)^-2 all over (x^-1 y^2 z^3)^1\2

2)(divide the rational expression and state the domain)

1-t \ 3t+t divided by t^2 -2t +1 \ 7t +21t^2

3)3x^2 - 3x=0

4)2-11i \ 4+i

5)factor : x^4n - y^4n

6) rationalize the denominator: 7- 2 radical 3 \ 4 - 5radical 3

sorry for so many but i need help, thank you guys

Answer 1

1) (x^2 y^-3 z^-1)^-2 / (x^-1 y^2 z^3)^(1/2)

Add indices for multiplication, subtract indices for division.

= (x^-4 y^6 z^2) / [x^(-1/2) y^1 z^(3/2)]

= x^(-7/2) y^5 z^(1/2)

2) [(1 - t) / (3t^2 + t)] / [(t^2 - 2t + 1) / (7t + 21t^2)]

= [(1 - t) / (3t^2 + t)] * [(7t + 21t^2) / (t^2 - 2t + 1)]

= [(1 - t) * (7t + 21t^2)] / [(3t^2 + t) * (t^2 - 2t + 1)]

= [(1 - t) * 7t(1 + 3t)] / [t(3t + 1) * (t - 1)^2]

= [-(t - 1) * 7t(1 + 3t)] / [t(1 + 3t) * (t - 1)^2]

= -7 / (t - 1)

= 7 / (1 - t)

3) 3x^2 - 3x = 0, or, 3x(x - 1) = 0, so, x = 0 or 1.

4) [(2 - 11i) / (4 + i)] * (4 - i) / (4 - i)

= (8 - 2i - 44i + 11i^2) / (16 - i^2)

= (-3 - 46i) / 17 (note: i^2 = -1)

= -3/17 - (46/17)i

5) x^(4n) - y^(4n)

= (x^n)^4 - (y^n)^4

Let a = x^n and b = y^n

= a^4 - b^4

= (a^2 - b^2)(a^2 + b^2)

= (a - b)(a + b)(a^2 + b^2)

= (x^n - y^n)(x^n + y^n)[x^(2n + y^(2n)]

6) [7 - 2sqrt(3)] / [4 - 5sqrt(3)]

Multiply top and bottom each by [4 + 5sqrt(3)] :

= [28 +35sqrt(3) - 8sqrt(3) - 30] / [16 - 75]

= [-2 + 27sqrt(3)] / (-59)

= [2 - 27sqrt(3)] / 59

Answer 2

I already answered this

1) (x^2 y^-3 z^-1)^-2 all over (x^-1 y^2 z^3)^1\2

part by part

(x^2 y^-3 z^-1)^-2

1 / (x^2 y^-3 z^-1)^2

1 / (x^4 y^-6 z^-2)

z^2y^6/x^4

(x^-1 y^2 z^3)^1\2

y^1 z^3/2 / x^1/2

combine

z^2y^6/x^4 * x^1/2 /y z^3/2

xyz, one at a time

z^2 / z^3/2 = z^(2-3/2) = z^1/2

x^4 * x^1/2 = x^(4+1/2) = x^9/2

y^6/y = y^5

combine again

(z^1/2)(x^9/2)(y^5)

3x^2 - 3x=0

factor

3x(x - 1) = 0

x = 0, 1

.