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Question

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

Answer 1

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

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