Rational Exponents & Relations

2012-12-17 12:02 am
Simplify the following.

please show all the clear steps.

1) (x^1/2 divide by x^1/3)times x^1/4

2) (x^3n over y^5)^1/2 times (x^n over y^3)^1/2

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Describe the relation in words.

3) (1,3),(2,5),(3,7),(4,9),(5,11)

Thanks

回答 (1)

2012-12-17 12:28 am
✔ 最佳答案
1)
{x^(1/2)/[x^(1/3)]}x^(1/4)
= x^(1/2 - 1/3 + 1/4)
= x^[(6 - 4 + 3)/12]
= x^(5/12)

2)
{[x^(3n)/(y^5)]^(1/2)}[(x^n)/(y^3)]^(1/2)
= x^(3n/2 + n/2) / y^(5/2 + 3/2)
= x^(2n)/(y^4)

3)
(1 , 3) , (2 , 5) , (3 , 7) , (4 , 9) , (5 , 11)
i.e. (n , 2n + 1) where n = 1, 2, 3, 4, 5
i.e. They are collinear on y = 2x + 1.
參考: Myself


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